Audrey deposited $40,000 in a savings account with simple interest. Five years later, she had earned $30,000 in interest. What was the interest rate? FIRST ONE TO ANSWER GETS BRANIEST

The value of the z-test statistic is 1.79.

We have,

In this sampling scenario, we are trying to test whether the average score on a nationwide biology examination is different from 501.

We took a random sample of 100 exam scores, and the sample mean (average) was found to be 515, with a standard deviation of 78.

To determine an appropriate test statistic, we consider two factors: the sample size and whether the population standard deviation is known.

Since the sample size is large (100), we can use the z-test statistic.

This test statistic helps us compare the sample mean to the hypothesized population mean (501) while considering the variability of the data.

The z-test statistic formula involves calculating the difference between the sample mean (515) and the hypothesized mean (501), and then dividing it by the standard deviation of the population divided by the square root of the sample size.

In this case, the known population standard deviation is 78, and the sample size is 100.

By plugging in these values, we find that the z-test statistic is 1.79.

This value indicates how many standard deviations the sample mean is away from the hypothesized mean.

In simple terms, the z-test statistic helps us assess whether the difference between the sample mean (515) and the hypothesized mean (501) is large enough to conclude that the average score on the nationwide biology examination is different from 501.

A higher absolute value of the z-test statistic suggests a stronger evidence for a difference between the population mean and the hypothesized mean.

Thus,

The value of the z-test statistic is 1.79.

Learn mroe about z-test statistics here:

https://brainly.com/question/30754810

#SPJ4

Therefore , the solution to the given problem of linear equation comes out to be T= 64.

Any function that fulfills the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both x and y are factors, the previous sentence is commonly referred to as an equation system with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations: x + z = 2, and 3z - y + z = 3 both have a zero solution. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is referred to as linear. The equation is written as Y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : 3+ T/2 = 35

thus,

=>  3+ T/2 = 35

=> T/2 = 35-3

=> T/2 = 32 *2

=> T= 64

Therefore , the solution to the given problem of linear equation comes out to be T= 64.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

Answer:

108 degrees

Step-by-step explanation:

3x+x+6x=10x, 180/10=18 and 18x6 is 108

The missing length in the given figure is 10 ft

In the figure there are two rectangle.

We have to find the missing length of the rectangle

The length of one rectangle is 16 ft.

The other length of rectangle is splitted to two parts

One length has 6 ft then the other length is 10 ft

Hence, the missing length in the given figure is 10 ft

To learn more on Area click:

https://brainly.com/question/20693059

#SPJ1

Answer:

The y-intercept represents the temperature at the start, before any time has passed.

In the scenario, y intercept represents the temperature which starts from 8 °F.

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

In the given graph,

x-axis shows time in hours,

And y-axis shows temperature in Fahrenheit.

Since, the y-intercepts shows the value where x=0, or the values of y-axis.

In the given graph,

The y-axis shows the temperature.

Therefore, y intercept represents the temperature which starts from 8 °F.

To know more about Graph on:

https://brainly.com/question/17267403

#SPJ2

Answer:

13m

Step-by-step explanation:

this is because she needs 130

Answer:

13 months

Step-by-step explanation:

subtract 120 from 250 because that is how much she already has and then divide that answer by ten which will give you the number of months

The sum of the series ∑[n=0, ∞] 10^n / (7^n n!) is e^(10/7) / 3.

To find the sum of the series ∑[n=0, ∞] 10^n / (7^n n!), we can use the Maclaurin series expansion of e^(10/7): e^(10/7) = ∑[n=0, ∞] (10/7)^n / n!

Multiplying both sides by e^(-10/7), we get:

1 = ∑[n=0, ∞] (10/7)^n / n! * e^(-10/7)

e^(-10/7) * ∑[n=0, ∞] (10/7)^n / n! = e^(-10/7) / (1 - 10/7) = 1/3

Therefore, the sum of the series ∑[n=0, ∞] 10^n / (7^n n!) is e^(10/7) / 3.

To learn more about “series” refer to the https://brainly.com/question/24643676

#SPJ11

Answer:

There would be 8 people in each bus.

Step-by-step explanation:

Answer:

49 students in each bus

Step-by-step explanation:

Answer:312 people

Step-by-step explanation:

Answer:

312

Step-by-step explanation:

78 x 4

Answer: 0.9

Step-by-step explanation:

Answer:

0.9 I think. Im only in 6th grade and i think thats the answer.

If Cynthia keeps up her pace, she will finish the 248-mile bike race in approximately 7.29 hours.

To determine how many hours Cynthia will finish the 248-mile bike race given her pace of 68 miles in 2 hours, follow these steps:

1. Calculate her speed by dividing the distance by the time:

speed = 68 miles / 2 hours

speed = 34 miles per hour.

2. Divide the total distance of the race (248 miles) by her speed (34 miles per hour) to find the time:

time = 248 miles / 34 miles per hour

time ≈ 7.29 hours.

Thus, we can state that if Cynthia keeps up her pace, she will finish the 248-mile bike race in approximately 7.29 hours.

To learn more about distance visit : https://brainly.com/question/26550516

#SPJ11

Answer :

55°

Detailed explanation:

The triangles are isosceles (having two sides of equal length and angle).

Hence solve for angle DCE

Angle DCE= 180°-(55°+55°)

=70°

As vertically opposite angles are equal. Thus,

angle ACB=70°.

Hence 180°-70°=110°

As the angles in an isosceles triangle are equal hence;

110°÷2=55°

Hence angle ABC is 55°

Hope this is has been clearly explained!

The measure of angle ABC from the given figure is 55 degree. Therefore, the correct answer is option A.

From the given figure, we have two isosceles triangles DCE and ABC.

In ΔDCE,

Base angle is ∠CED=55°.

Here, base angles are equal

That is, ∠CED=∠CED=55°

By using angle sum property of a triangle, we get

∠DCE=180°-(55°+55°)

∠DCE=70°

Now, ∠DCE and ∠ACB are vertically opposite angles are equal.

So, ∠DCE =∠ACB=70°

In ΔABC, base angles BAC and ABC are equal

So, ∠BAC+∠ABC+∠ACB=180°

∠ABC+∠ABC+70°=180°

2∠ABC=110°

∠ABC=55°

Therefore, the correct answer is option A.

To learn more about the angle sum property of a triangle visit:

https://brainly.com/question/8492819.

#SPJ4

Answer:

Step-by-step explanation:

You don't need the Law of Cosines, the Law of sines if what you need. You can't use the Law of Cosines because in order to find side a, you would need the length of side c and you don't have it. Using the Law of Sines is appropriate, knowing that angle B = 55:

\(\frac{sin55}{175}=\frac{sin42}{a}\) and solving for a:

\(a=\frac{175sin42}{sin55}\) so

a = 143.0

(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

Read more about Linear Function at; https://brainly.com/question/4025726

#SPJ1

Answer:

\(x {}^{2} \times + 4x\)

Step-by-step explanation:

\(f(x + 4) = (x + 4) {}^{2} - 3(x + 4) - 4 \\ = x {}^{2} + 8x + 16 - 3x - 12 - 4 \\ = x {}^{2} + 4x\)

Answer:

120 cm^2.

Step-by-step explanation:

The area of one triangle = 1/2 * base * height

= 1/2 * 8 * 6

= 1/2 * 48

= 24 cm^2

So area of the pentagon = 5 * 24

= 120 cm^2.

The value of x in the equation will be C. x = 1/3

It should be noted that from the information given, the equation given is illustrated as:

2(6x - 2) = -8

12x - 4 = -8

12x = -8 + 4

12x = -4

Divide both side by 12

12x/12 = -4/12

x = -1/3

Since absolute value is non negative, the value is 1/3.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

The first answer

Step-by-step explanation:

Domain refers to the set of x values and range refers to the set of y values. Since x goes from 0 to 3, and does not exclude any values within those numbers, the first answer applies to that set.

Answer:

option 1

that is

{t| 0 <= t <= 3}

Step-by-step explanation:

as the graph plots height ove time

time will be the domain, taken on the x axis, with values ranging from 0 to 3.

so the domain is

{t| 0 <= t <= 3}

Answer:

I think it's 6 or 0.6

Answer:

=22 m²

Step-by-step explanation:

Total area= Area of rectangle 1 + Area of rectangle 2

Answer:

45

Step-by-step explanation:

6^2 + 3√9

=36 + (3 x 3)

=36 + 9

= 45

Answer:

45

Step-by-step explanation:

6^2 = (6x6)

36+3 √9

you can simplify √9 to 3

36+3(3)

36+9

45

Answer:

9/49

Step-by-step explanation:

4 purple beads and 3 green beads= 7 beads

P( green) = green = total = 3/7

Replace the bead

4 purple beads and 3 green beads= 7 beads

P( green) = green = total = 3/7

P( green , replace, green) = 3/7 * 3/7 = 9/49

Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

To know more about trigonometry visit:

https://brainly.com/question/11550042

#SPJ4

Answer: c

Step-by-step explanation: 23/99 as a fraction

Answer:

$63.30

Step-by-step explanation:

Assuming the $60 is excluding taxes:

60 * 1.055 = $63.30

The expected count that can be deduced from the arrivals to the second compartment will be 200.

It should be noted that in order to perform a goodness of fit test, the expected number of rats that are in each compartment will be gotten.

Therefore, the expected number of rats that will be in the second compartment will be:

= 1/5 × 1000

= 200

In conclusion, the correct option is 200.

Learn more about expected count on:

https://brainly.com/question/1314739