Juanita decided to start saving for college. She deposited $500 into an account which earns 4% simple annual interest. How much will she have in her account after the end of the three years?

A: $60.00

B: $440.00

C: $560.00

D: 562.43​

Answer:

10+20x-12

20x-2

X=20-2

X=18

Answer:

x = 15; y = 21

Step-by-step explanation:

The vertical angles have the same measure.

The sum of the measures of the angles of a triangle is 180 deg.

Left triangle:

4y - 18 + y + 14 + 6x - 11 = 180     Equation 1

Right triangle:

6x - 11 + 81 + x + 5 = 180       Equation 2

Simplify Equation 1.

4y - 18 + y + 14 + 6x - 11 = 180

6x + 5y = 195      Equation 3

Simplify Equation 2.

6x - 11 + 81 + x + 5 = 180

7x = 105

Solve last equation for x.

7x/7 = 105/7

x = 15

Substitute 15 for x in Equation 3 and solve for y.

6x + 5y = 195

6(15) + 5y = 195

90 + 5y = 195

5y = 105

y = 21

Answer: x = 15; y = 21

Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

a. Null hypothesis: H₀: µ ≤ 74

b. A t-test is appropriate here because the population standard deviation is not known, and the sample size is less than 30.

c. The value of Test statistic is -6.325

d. At a 0.05 significance level, the critical value for a right-tailed test is  -1.664.

e. The test statistic (-4.38) is less than the critical value (1.645). Hence we can reject the null hypothesis.

a. Null hypothesis, H0: µ = 74, alternative hypothesis, H1: µ > 74  (there is no significant difference in the mean job satisfaction scores of employees after the telecommuting policy is adopted).

b. A t-test is appropriate here because the population standard deviation is not known, and the sample size is less than 30. This is a one-tailed test because the alternative hypothesis is directional (i.e., it states that the mean level of satisfaction will increase with telecommuting).

c. The test statistic is calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size.  Substituting the values given in the question: t = (56 - 74) / (8 / √80) = -6.325

d. The critical value for a one-tailed t-test with 79 degrees of freedom at the 0.05 level of significance is -1.664. Since the calculated t-value of -6.325 is less than the critical value of -1.664, we reject the null hypothesis.

e. Based on the calculated t-value and critical value, we reject the null hypothesis that the mean level of satisfaction is the same before and after telecommuting and accept the alternative hypothesis that telecommuting increases the mean level of satisfaction among employees.

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In every triangle the addition of all internal angles is always 180 degrees.

So this means we can build this equation

5x + 35 + 60 = 180

now separate x values and numerical values

5x = 180 - 60 - 35

x= (180 - 60 - 35)/ 5 = 85/5 = 17

Answer:

Step-by-step explanation:

2x+3

x=3divides2

Some cats may prefer different types of litter or litter box placements, so it's always best to observe your cats' behavior and adjust accordingly.

The general guideline of having one litter box per cat plus one extra in multi-cat households is to ensure that all cats have access to a clean and comfortable litter box,  which is essential for their health and well-being. Cats are very clean animals by nature, and they tend to avoid using dirty or smelly litter boxes. In a multi-cat household with only one or a few litter boxes, there may be competition between cats for access to the litter box, leading to conflicts and inappropriate elimination outside the litter box.

Having enough litter boxes also helps prevent the buildup of waste and odors, which can be unhealthy for both cats and humans sharing the same living space. It's important to note that this guideline is not a hard and fast rule and may vary depending on factors such as the size of the house, the number of floors, and the cats' individual preferences. Some cats may prefer different types of litter or litter box placements, so it's always best to observe your cats' behavior and adjust accordingly.

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The approximate length of ab is 12.2 feet

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the other two sides' lengths.

It can be written as c2 = a2 + b2 where c is the hypotenuse's length and a and b are the other two sides' lengths. Pythagoras, a Greek mathematician, is credited with discovering the theorem, which bears his name.

The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, can be used to estimate the length of AB (the hypotenuse).

The distances along the room's 11-foot and 13-foot sides serve as the two shorter sides in this situation, while AB serves as the hypotenuse. AB is around the following length:

√(11^2 + 13^2 + 10^2) = √(146) = 12.2 feet

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Answer:

All except 2,5,3

Step-by-step explanation:

To make a triangle, two of the side lengths added together should always be larger than the third side length. Otherwise, the triangle could not be formed since the sides could not reach each other. This means that the sides 2,5,3 cannot work. Hope this helps!

Answer:

Root is a fancy word for a zero.

Using the quadratic formula you will get

x = 1.2, -.25

B is the correct answer. (-1/4)

The values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

To make the function both continuous and differentiable everywhere, we need to find the values of a and b that make the two parts of the piecewise function equal at x=-1. This will ensure that there are no jumps or breaks in the function at x=-1, making it continuous and differentiable.

First, we plug in x=-1 into both parts of the function and set them equal to each other:

3−3(-1) = -2/3(-1)^2 + a(-1) + b

Simplifying both sides gives us:

6 = -2/3 + a + b

Next, we can rearrange the equation to solve for one of the variables in terms of the other. Let's solve for b in terms of a:

b = 20/3 - a

Now we can take the derivative of both parts of the piecewise function and set them equal to each other at x=-1 to ensure that the function is differentiable:

-3 = -4/3x + a

Plugging in x=-1 gives us:

-3 = 4/3 + a

Rearranging to solve for a gives us:

a = -13/3

Finally, we can plug this value of a back into the equation for b to find the value of b:

b = 20/3 - (-13/3) = 33/3 = 11

So the values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

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Answer:

50 years

Step-by-step explanation:

use the simple interest formula :

PRT/100

P is the principle (5000)

R is the rate of interest (4)

T is the time taken (x- unknown)

the amount at the end is double the amount invested  = 5000*2 = 10000

(5000*4 * x )/100 = 10000

20000x/100=10000

20000x = 100*10000

20000x = 1 000 000

x= 1 000 000/ 20 000

x = 50

it will take 50 years

Answer:

50 years

Step-by-step explanation:

The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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Answer:

C. The slope from point O to point A is fraction 1 over 3 times the slope of the line from point A to point B.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

log3(3^4) = x.

=> 3^x = 3^4

=> x = 4.

Answer:

2 v 13, 2 Square root 13

Step-by-step explanation:

there's 2 right triangles

a)

10^2 = 6^ + a^2

100 - 36 = a^2

64 = a ^2

a = 8

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

now we know the base of the right triangle = 8

and also the base of the left one = 4

8 + 4 = 12

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

now find x

b)

x^2 = 6^2 + 4^2

x^2 = 36 + 16

x^2 = 52

x = (square root) 52

x = 2 v 13     <---- "v = square root"

Instructions :- Simplify the answer if there is square root

hypotenuse² = perpendicular²+base²

First triangle:-

\( {h}^{2} = {p}^{2} + {b}^{2} \\ {10}^{2} = {6}^{2} + {b}^{2} \\ 100 = 36 + {b}^{2} \\ 100 - 36 = {b}^{2} \\ 64 = {b}^{2} \\ 8 = b\)

Second triangle

\( {h}^{2} = {p}^{2} + {b}^{2} \\ {x}^{2} = {6}^{2} + {4}^{2} \\ {x}^{2} = 36 + 16 \\ {x}^{2} = 52 \\ x = \sqrt{52} = 7.2 \\ x = 7 \: \: approx\)

The number to add to the set of data is 26

The set of data is given as:

11,14,23 and 16

Let the new number be x

So that

Mean = 18

Mean is calculated as:

Mean = Sum/Count

So, we have:

(11 + 14 + 23 + 16 + x)/5 = 18

Multiply by 5

11 + 14 + 23 + 16 + x = 90

Evaluate the like terms

x = 26

Hence, the number to add is 26

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Complete question

A set of data already has the values 11, 14, 23, and 16. What value would have to be added to the set for the mean of the five numbers to be 18?

Line QT has a 5 unit length.

A line is a geometric object with an endless length and no breadth, depth, or curvature.

Lines are one-dimensional objects since they can exist in two, three, or higher-dimensional regions.

A line segment with two points indicating its endpoints is also referred to as a line in daily speech.

So, using the relationship between the sides of comparable triangles, we have the following.  ΔRST and  ΔRPQ:

   ST/RT = PQ/QR

   RQ = QT + RT

Then,

   ST/RT = PQ/QT + RT

Then, we obtain:

   QT + 5/RT = PQ/QT + RT

Given that QT is the natural number then, QT = 5 units.

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Based on the above, the capacity of a 5-liter tin is about  500 cm³.

To be able to convert the capacity of a 5-liter tin to its volume in cm³, One need to use the conversion factor that is, 1 liter is equivalent to 100 cm³.

So, to be able to calculate the volume of a 5-liter tin in cm³, one have to multiply the capacity (5 liters) by the conversion factor (100 cm³/liter):

Volume in cm³ = 5 liters x 1000 cm³/liter

                           = 500 cm³

Therefore, the capacity of a 5-liter tin is about  500 cm³.

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See full text below

Convert the capacity of a 5 litre tin to its volume in cm³.1litre is equivalent to 100cm³

The location of the values square root of 11, square root of 8, and twenty two ninths on the number line is illustrated below.

It should be noted that a number line simply means a straight line that serves as an abstraction for real numbers.

It should be noted that square root of 11 will be 3.316. The square root of 8 is 2.83 and twenty two ninths on the number line will be around 20.22.

This is important to know the place where each falls on the number line.

Note that an overview was given.

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The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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Answer:

bmw 3 highest lowest bmw 7 largest range bmw 5

Step-by-step explanation:

Answer:

4/5+14%15

4×3/5+14×1/15

12+14/15

26/15

(26/5)/2

13/15

Answer:ay

Step-by-step explanation:

yaaaaaaaaaaaaaaaaaaaaaaaaaa

The solution to the system of equation is (7/5, 22/5)

Given the system of equation as shown below;

4x + y = 10 * 2

3x - 2y = 13 * 1

_____________

8x + 2y = 20

3x - 2y = 13

Subtract

8x - 3x = 20 - 13

5x = 7

x = 7/5

Substitute the value of x into any of the equation

4x + y = 10

4(7/5) + y = 10

28/5 + y = 10

y = 10 - 28/5

y = 22/5

Hence the solution to the system of equation is (7/5, 22/5)

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Step-by-step explanation:

Since right angle is equal to 90°,

90°-55°=35°

Question:

Jordyn, Teri, and Morgan are going to have a kite-flying contest. Jordyn and Teri each have one roll of kite string. They also each have 45 yards of extra string. Morgan has three rolls of kite string plus 10 yards of extra string. All the rolls of string are the same length. The girls want to see who can fly their kite the highest.

Since Jordyn and Teri have fewer rolls of kite string, they decide to tie their string together, so their kite can fly higher. Write at least two expressions to show how much kite string Jordyn and Teri have. Let x represent the number of yards of string on one roll.

Answer:

\(y=x +45\)

\(y = 45 + x\)

Step-by-step explanation:

From the complete question, we have:

Jordyn & Teri

\(Rolls = 1\)

\(Extra = 45\ yd\)

Morgan

\(Rolls = 3\)

\(Extra= 10\ yd\)

Required

Expression for Jordyn and Morgan

Let the total kite by Jordyn and Teri be represented with y

This is calculated as:

\(y = Rolls + Extra\ Yard\)

This gives:

\(y = 1\ roll + 45yd\)

1 roll is represented with x.

So:

\(y=1x +45\)

\(y=x +45\)

This can be rewritten as:

\(y = 45 + x\)

Answer:

x² + y² = 9

Explanation:

circle formula: (x -h)² + (y - k)² = r²

where (h, k) is the center, r is radius

Here given for center: (0, 0)

Identify

Equation of circle: