Leshawn has $580 in a savings account that pays 3% interest.
How much interest will be earned in 5 years?
How much interest will be earned in 6 months?

The obtained value must be compared against the critical value. Hence, the correct option is b.

In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.

After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.

If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.

If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.

Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.

To know more about critical value refer here:

https://brainly.com/question/32389590#

#SPJ11

(i) To find the solution for yt in the given equation yt = yt−1 + εt + 0.3εt−1, we can rewrite it as yt - yt−1 = εt + 0.3εt−1. By applying the lag operator L, we have (1 - L)yt = εt + 0.3εt−1.

Solving for yt, we get yt = (1/L)(εt + 0.3εt−1). The solution for yt involves lag operators and depends on the values of εt and εt−1.  (ii) For the equation yt = 1.2yt−1 + εt, to find the s-step-ahead forecast Et[yt+s], we can recursively substitute the lagged values. Starting with yt = 1.2yt−1 + εt, we have yt+1 = 1.2(1.2yt−1 + εt) + εt+1, yt+2 = 1.2(1.2(1.2yt−1 + εt) + εt+1) + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to ensure that the coefficient on yt−1, which is 1.2 in this case, is less than 1 in absolute value. If it is greater than 1, the process will be explosive and not stationary. To achieve stationarity, we can either decrease the value of 1.2 or introduce appropriate differencing operators.

(iii) For the equation yt = yt−1 + t + εt, finding the solution for yt and the s-step-ahead forecast Et[yt+s] involves incorporating the time trend t. By recursively substituting the lagged values, we have yt = yt−1 + t + εt, yt+1 = yt + t + εt+1, yt+2 = yt+1 + t + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to remove the time trend component. We can achieve this by differencing the series. Taking first differences of yt, we obtain Δyt = yt - yt-1 = t + εt. The differenced series Δyt eliminates the time trend, making the model stationary. We can then apply forecasting techniques to predict Et[Δyt+s], which would correspond to the s-step-ahead forecast Et[yt+s] for the original series yt.

Learn more about model here: brainly.com/question/19426210

#SPJ11

The three possibilities that Damon can use as the common factor for equivalent expression are y(5xz + 3z + 2x), z(5xy + 3y + 2x) and  xy(5z + 3 + 2z).

To discover a common figure for 60xyz+36yz+24xy, we have to be discover the Greatest Common Factor (GCF) of the coefficients 60, 36, and 24, and the factors x, y, and z.

The GCF of the coefficients 60, 36, and 24 is 12. Able to calculate out 12 from each term:

60xyz+36yz+24xy = 12(5xyz + 3yz + 2xy)

Presently, we ought to discover a common calculate for the remaining components, 5xyz + 3yz + 2xy. Here are three conceivable outcomes:

Calculate out y:

5xyz + 3yz + 2xy = y(5xz + 3z + 2x)

Calculate out z:

5xyz + 3yz + 2xy = z(5xy + 3y + 2x)

Calculate out xy:

5xyz + 3yz + 2xy = xy(5z + 3 + 2z)

So, Damon may utilize any of these three conceivable outcomes as the common calculate for an proportionate expression.

Learn more about  common factor here: https://brainly.com/question/25266622

#SPJ1

Answer:

See below

Step-by-step explanation:

Look at 100th place   if   it is ≥5   round the 10th place up by 1  o/w leave it alone

22.7

22.8

22.8

22.7

22.8

22.7

Answer: q = 16

Step-by-step explanation:

When given the equation 3(q - 7) = 27,  you would solve for the variable.

The variable in this equation is q, so we need to isolate the variable.

Solving process:

3(q - 7) = 27

lets distribute, due to the orders of PEMDAS.

PEMDAS stands for: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

3(q - 7) = 27

distributing is multiplying the number correlated outside of the parenthesis with the inside components.

3q - 21 = 27

lets add 21 to both sides

3q = 48

now lets divide by 3 (we are trying to get q by itself)

q = 16

----

To check if your solution is correct, you replace the value (16) of the variable (q) within the original equation:

3 (16 − 7) = 27

Following PEMDAS you get:

3(9) = 27

27 = 27 (meaning that the solution is correct)

Thank you.

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

hope it helps! :)

Answer:

(2,9) , (3,8) , (4,7) , (5,6)

Step-by-step explanation:

ab+ba = 10a+b+10b+a = 11a+11b = 11(a+b)

if a+b = 11 then ab+ba = 11²

(a,b) or (b,a) : (2,9) , (3,8) , (4,7) , (5,6)

check: 29+92 = 121 = 11²

56+65 = 121 = 11²

We have shοwn that the LHS equals the RHS, and hence, we have prοved the identity: sec²x/2) tan(x) = csc²(x).

Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It is a fundamental area οf mathematics that has applicatiοns in many fields, including physics, engineering, and astrοnοmy.

Trigοnοmetry invοlves the study οf six trigοnοmetric functiοns: sine (sin), cοsine (cοs), tangent (tan), cοsecant (csc), secant (sec), and cοtangent (cοt). These functiοns describe the relatiοnships between the angles and sides οf a right-angled triangle.

Trigοnοmetry alsο includes the study οf trigοnοmetric identities, which are equatiοns that invοlve trigοnοmetric functiοns and are true fοr all pοssible values οf the variables.

In the given question,

Starting with the left-hand side (LHS) of the given identity:

sec²(x/2) tan(x)

Using the identity, sec²(x) = 1/cos²(x), we can write:

sec²(x/2) = 1/cos²(x/2)

Substituting this into the LHS:

1/cos²(x/2) * tan(x)

Now, using the identity, tan(x) = sin(x)/cos(x), we can write:

1/cos²(x/2) * sin(x)/cos(x)

Rearranging and simplifying:

sin(x) / cos(x) * 1/cos²(x/2)

Using the identity, csc(x) = 1/sin(x), we can write:

1/sin(x) * 1/cos(x) * 1/cos²(x/2)

Now, using the identity, cos(2x) = 1 - 2sin²(x), we can write:

cos(x) =√(1 - sin²(x/2))

Substituting this into the above equation:

1/sin(x) * 1/√(1 - sin²(x/2)) * 1/cos²(x/2)

Simplifying:

1/sin(x) * 1/√(cos²(x/2)) * 1/cos²(x/2)

Using the identity, csc²(x) = 1/sin²(x) and simplifying:

csc²(x) * cos²(x/2) / cos²(x/2)

The cos²(x/2) terms cancel out, leaving:

csc²(x).

Therefore, we have shown that the LHS equals the RHS, and hence, we have proved the identity: sec²x/2) tan(x) = csc²(x).

To know more about Trigonometry, visit:

https://brainly.com/question/29002217

#SPJ1

Answer:

\(2^{3x+3}\)

Step-by-step explanation:

to divide exponents with the same base you just subtract them

(4x+4)-(X+1)

4x+4-x-1

3x+3

Hopes this helps please mark brainliest

Answer:

frac{16x+4}{2^{x}+1 =

Step-by-step explanation:

Evaluate the exponent! hope this helped

Answer:

Step-by-step explanation:

Given that:

To Find:

Let us assume:

Finding the number of T-shirts bought:

According to the question.

Rate × Pieces of T-shirts = Rate × Pieces of T-shirts

⟶ 210 × 16 = 280 × x

⟶ 3360 = 280x

⟶ x = 3360/28

⟶ x = 12

Hence,

Answer:

0.9985

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Given the expression:

To factor the given expression, we need two numbers the product of them = 100 and the sum of them = 20

We will factor the number 100

100 = 1 x 100 ⇒ 1 + 100 = 101

100 = 2 x 50 ⇒ 2 + 50 = 52

100 = 4 x 25 ⇒ 4 + 25 = 29

100 = 5 x 20 ⇒ 5 + 20 = 25

100 = 10 x 10 ⇒ 10 + 10 = 20

So, the suitable numbers are 10, 10

so, the factorization will be as follows:

The given expression is a complete square.

So, the answer will be (u+10)(u+10)

Or can be written as (u+10)²

Answer:

7/2

Step-by-step explanation:

y2-y1/x2-x1

(6-(-1)/8-6) = 7/2

Answer:

x = -18, y = 14

Step-by-step explanation:

4x + 6y = 12

x + 2y = 10

Divide both sides of the first equation by 2. Write the second equation below it.

2x + 3y = 6

x + 2y = 10

Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Then add the equations eliminating x.

      2x + 3y = 6

(+)  -2x - 4y = -20

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

             -y = -14

y = 14

Substitute 14 for y in the second equation and solve for x.

x + 2y = 10

x + 2(14) = 10

x + 28 = 10

x = -18

Solution: x = -18, y = 14

Sum of two function f(x) and g(x) is -12x³+12x²-11x+2

A mathematical expression that indicates a relationship between independent variable and dependent variable. If x is an independent variable function is denoted by f(x) or g(x).

we are given two functions f(x)= -8x³+9x²-7x+8

                                           g(x)= -4x³+3x²-4x-6

now we need to add these two. f(x)+g(x)= -12x³+12x²-11x+2

hence, we obtain another function.

to know more about function visit:

https://brainly.com/question/21145944

#SPJ1

-8 = -7 + X

- 8 + 7 = X (Adding 7 to both sides of the equation)

-1 =x (Subtracting)

The answer is x=-1.

the answer of -8 = -7 +Xx is x= -1

it’s 1/4 of a circle.

The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.

According to the question,

We have the following information:

Cost of a quarter-page ad cost = $110

Mark down in the price = 15%

Now, q represents the price of a quarter-page ad after the markdown.

(Note that when we remove the sign of % means that the number has to be divided by 100.)

So, the equation will be the difference of the markdown price from the original price:

q = 110-(15/100)110

q = 110-0.15*110

q = 110-0.15(110)

Hence, the correct option is the third one.

To know more about equation here

https://brainly.com/question/13287605

#SPJ1

∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

To find ∂z/∂s and ∂z/∂t, we use the chain rule of partial differentiation. Let's begin by finding ∂z/∂s:

∂z/∂s = (∂z/∂)(∂/∂s)[(st9) cos(s9t)]

We know that ∂z/∂ is cos()cos() - sin()sin(), and

(∂/∂s)[(st9) cos(s9t)] = t9 cos(s9t) + (st9) (-sin(s9t))(9t)

Substituting these values, we get:

∂z/∂s = [cos()cos() - sin()sin()] [t9 cos(s9t) - 9st2 sin(s9t)]

Simplifying the expression, we get:

∂z/∂s = -sin()cos()t9 + cos()sin()9st2

Similarly, we can find ∂z/∂t as follows:

∂z/∂t = (∂z/∂)(∂/∂t)[(st9) cos(s9t)]

Using the same values as before, we get:

∂z/∂t = [cos()cos() - sin()sin()] [(s) (-sin(s9t)) + (st9) (-9cos(s9t))(9)]

Simplifying the expression, we get:

∂z/∂t = sin()cos()s - cos()sin()81t

Therefore, ∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

Learn more about chain rule here:

https://brainly.com/question/28972262

#SPJ11

A sample size of approximately 9604 citizens is needed to achieve at least 95% confidence that the estimate is within 1% of the true percentage.

To determine the sample size needed for a study to estimate the percentage of citizens in a town who favor water fluoridation with 95% confidence and a margin of error within 1%, you can use the following formula:

Sample Size (n) = (\(z^{2}\) * P * (1-P)) / \(E^{2}\)

where:
Z = 1.96 (the Z-score corresponding to a 95% confidence level)
P = estimated proportion of the population (use 0.5 if no prior knowledge)
E = margin of error (0.01 for 1%)

Plugging the values into the formula:

n = (\(1.96^{2}\) * 0.5 * (1-0.5)) / \(0.01^{2}\)
n = (3.8416 * 0.5 * 0.5) / 0.0001
n = 0.9604 / 0.0001
n ≈ 9604

Therefore, a sample size of approximately 9604 citizens is needed to achieve at least 95% confidence that the estimate is within 1% of the true percentage.

Know more about   sample size   here:

https://brainly.com/question/30647570

#SPJ11

when k = 4, the function x + k/x will have a relative maximum at x = -2.

To find the value of k that will make x+k/x have a relative maximum at x=-2, we can use the first derivative test.

First, we find the derivative of x+k/x with respect to x:

f'(x) = 1 - k/x^2

Next, we set x = -2 and solve for k to make f'(-2) = 0:

f'(-2) = 1 - k/(-2)^2 = 1 - k/4

1 - k/4 = 0

k = 4

what is derivative?

A derivative is a mathematical concept that represents the rate at which a function changes over time or space. It is the slope of a tangent line to a curve at a particular point.

In other words, the derivative of a function f(x) at a point x=a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim[h→0] [f(a+h) - f(a)]/h

The derivative gives us information about how quickly the function is changing at a specific point.

To know more about derivative visit:

brainly.com/question/29144258

#SPJ11

Answer:

the scale factor is times 0.5

Explanation:

20 plus 10 is 30. Half of 20 is 10 so that is 0.5

It is also like that for the others

Answer:

0.1009

Step-by-step explanation:

To convert percentage into decimal, you need to divide the percentage by 100

10.09/100

= 0.1009

Assuming that ΔABC has equal sides AB and AC, we can say that AD is parallel to BC hence∠A=∠B.

What is Congruency?

ongruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

from △ABD and △ACD,

AB=AC ,AD is common

∠ADB=∠ADC, since both are right angles.

by SSA congruence

△ABD≅△ACD

therefore base angles are equal.

use sine rule,

a/sinA = b/sinB = c/sinC

by definition of isosceles triangle, any two sides are equal

w.l.o.g. let, a=b

asinA=asinB=csinC

asinA=asinB

aa=1=sinAsinB

⟹sinA=sinB

and ∠A and ∠B are less than 180.

therefore ∠A=∠B

Learn more about congruent click here:

https://brainly.com/question/2938476

#SPJ4

In conclusion, the decision rule for rejecting the null hypothesis is that if the sample mean is greater than 1.96, the null hypothesis should be rejected, meaning the valve performs above the specifications.

To determine the decision rule for rejecting the null hypothesis, we first must identify the null and alternative hypotheses. The null hypothesis (H0) is that the valve performs at the specifications, meaning the mean pressure is 5.1 pounds/square inch. The alternative hypothesis (HA) is that the valve performs above the specifications, meaning the mean pressure is greater than 5.1 pounds/square inch.

Next, we can calculate the test statistic. The test statistic for this hypothesis test is the sample mean, which is 5.4 pounds/square inch.

To determine the decision rule, we compare the test statistic to the critical value from the z-table. The z-score for the critical value for a level of significance of 0.025 is 1.96. Therefore, the decision rule is that if the test statistic is greater than 1.96, reject the null hypothesis, meaning the valve performs above the specifications.
for such more questions on sample mean

https://brainly.com/question/26952915

#SPJ11

Answer:

square root of 10

Step-by-step explanation:

since triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units, therefore the square root will be 10

The length of A'T' is √10

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

Given:

TC = √17

AC = √5

AT = √10

as, ΔCAT with vertices A(-2, 1)

T (1, 4) and C(0, 0) .

so, there is translation without any shifting in terms of up and down.

Hence, the length of A'T' also be as AT = √10 units.

Learn more about translation here:

https://brainly.com/question/28240374

#SPJ2