Advertising A bank manager wants to encourage new customers to open accounts with principals of
at least $2,500. He decides to make a poster advertising a simple interest rate of 3%. What must the
principal be if the bank manager also wants to advertise that one can eam $10 the first month? Can
the poster correctly say, "Open an account of $2,500 and earn at least $10 interest in 1 month!"?
Explain your answer (be careful he said 1 MONTH).

Answer:

x and y = 66.5

Step-by-step explanation:

180-47=133

133/2=66.5

Answer:

Marty is correct.

Step-by-step explanation:

Marty is correct. A rhombus is a quadrilateral with four congruent sides, which also makes it a parallelogram, since it has opposite sides parallel. Additionally, a rhombus is a kite, since it has two pairs of adjacent congruent sides. Therefore, a rhombus meets the definition of a parallelogram and a kite, and Marty's statement is valid.

Answer:

Marti is NOT correct, a rhombus is not a kite.

Step-by-step explanation:

A rhombus is not a kite, all sides of a rhombus are equal, all sides of a kite are NOT equal.

There are various differences between a rhombus and a kite.

The given equations of planes are: 15x - 3y + 12z = 2  & 2y = 10x - 8z

To determine whether these planes are parallel, perpendicular or neither, we need to compare the normal vectors of the planes. The normal vector of a plane is given by the coefficients of x, y and z in the equation of the plane.

The normal vector of the first plane (1) is [15, -3, 12] and the normal vector of the second plane (2) is [10, 2, -8/2] = [10, 2, -4].

Now, to check if the planes are parallel or perpendicular, we can take the dot product of the normal vectors. If the dot product is 0, then the planes are perpendicular, and if it is non-zero, then the planes are parallel.

The dot product of the normal vectors of the given planes is:

[15, -3, 12] · [10, 2, -4] = (15)(10) + (-3)(2) + (12)(-4) = 0

Since the dot product is zero, the planes are perpendicular to each other.

To learn more about planes click here :

brainly.com/question/13792781

#SPJ11

Answer:

y intercept is 3 and slope is 4/1

Step-by-step explanation:

Answer:

25.2

Step-by-step explanation:

6/5 is 1.2, so it takes 1.2 minutes to run one lap.

This means 21 x 1.2 = the minutes it takes to run 21 laps around the track.

Therefore it takes 25.2 minutes to run around the track 21 times.

Answer:

(x+7)(x+9)

Step-by-step explanation:

(x+7)(x+9)

Apply the distributive property by multiplying each term of x+7 by each term of x+9.

x^2+9x+7x+63

Combine 9x and 7x to get 16x.

x^2+16x+63

To find the radius of convergence, we can use the ratio test for power series. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges if L < 1 and diverges if L > 1. Answer :  the interval of convergence, I, is [-1, 1] in interval notation.

Let's apply the ratio test to the given series:

lim(n→∞) |(8(-1)^(n+1)(n+1)x^(n+1)) / (8(-1)^n nx^n)|

Simplifying the expression, we get:

lim(n→∞) |(n+1)x / n|

Taking the absolute value, we have:

lim(n→∞) |(n+1)x / n| = |x|

For the series to converge, we need |x| < 1. Therefore, the radius of convergence, R, is 1.

To find the interval of convergence, we consider the endpoints of the interval. When |x| = 1, the series may or may not converge depending on the specific value of x. To determine the convergence at the endpoints, we can substitute x = 1 and x = -1 into the series and check for convergence.

For x = 1, the series becomes:

Summation of 8(-1)^n n, going to infinity, n=1

This is an alternating series that satisfies the conditions for convergence by the alternating series test. Therefore, the series converges when x = 1.

For x = -1, the series becomes:

Summation of -8(-1)^n n, going to infinity, n=1

This is also an alternating series that satisfies the conditions for convergence by the alternating series test. Therefore, the series converges when x = -1.

Hence, the interval of convergence, I, is [-1, 1] in interval notation.

Learn more about ratio  : brainly.com/question/31945112

#SPJ11

Answer:

The solution is (x = 6, y = -3)

Step-by-step explanation:

\(\sf \frac{x}{y + 1} = - 3 \: \: ........(1) \\ \\ \sf \frac{y}{x - 3} = - 1 \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \sf x + 3y = - 3 \: ........(1) \\ \\ \sf x + y = 3 \: \: \: \: \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \: \: \: \sf x + 3y = - 3 \: \: \: \: \: | \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x + y = 3 \: \: \: \:\: \: \: \: | \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9

A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.

The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.

Complete Question:

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.

Read more about hypothesis on:

https://brainly.com/question/25263462

#SPJ4

Answer:

lol

Step-by-step explanation:

The percentage that each expense has out of the total budgeted amount of $45,000  have been computed, where insurance has 8.00%, Utilities 7.00% and so on.

What is a percentage?

In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense

Insurance=$3600/$45,000=8.00%

Utilities=$3150/$45,000=7.00%

Clothing=$2700/$45000=6.00%

Transportation=$1350/$45000=3.00%

Entertainment=$5400/$45000=12.00%

Savings=$4050/$45000=9.00%

Taxes=$7200/$45000=16.00%

Food=$7650/$45000=17.00%

Housing=$9900/$45000=22.00%

Find out more about percentage on:https://brainly.com/question/16865197

#SPJ1

Answer:

x = 3, x = 4

Step-by-step explanation:

Given

\(\frac{24}{x}\) = 14 - 2x ( multiply through by x , x ≠ 0 )

24 = 14x - 2x² ( subtract 14x - 2x² from both sides )

2x² - 14x + 24 = 0 ( divide through by 2 )

x² - 7x + 12 = 0 ← in standard form

(x - 3)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

True. When modeling E(y) with a single qualitative independent variable, we use 0-1 dummy variables in the model. The number of dummy variables is equal to the number of levels of the qualitative variable minus one.

1. Identify the qualitative independent variable with multiple levels.

2. Determine the number of levels in the qualitative variable. Let's denote this number as "n".

3. Subtract one from the number of levels, resulting in n-1.

4. Create n-1 0-1 dummy variables to represent the different levels of the qualitative variable.

5. Assign a value of 1 to the corresponding dummy variable if the observation belongs to that level and assign a value of 0 to all other dummy variables.

6. Include these dummy variables in the regression model to estimate the effect of each level on the dependent variable.

7. The coefficients associated with the dummy variables represent the difference in the expected value of the dependent variable between each level and the reference level (the level not represented by a dummy variable).

Learn more about qualitative  : brainly.com/question/29004144

#SPJ11

Answer : x = 30 degrees

< JKL and < MKQ are complementary

Let < MKQ = x

Angle JKL is twice the measure of angle MKQ

JKL = 2 x MKQ

Sum of a complementary angles = 90 degrees

< JKL + < MKQ = 90

< JKL = 2MKQ

Substitute the value of < jkl

2(<2MKQ + Since, Therefore,

2x + x = 90

3x = 90

Divide both sides by 3

3x / 3 = 90/3

x = 30 degrees

To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.

Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.

Step 1: Determine the step size, h.

Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.

Step 2: Calculate the approximations within each subinterval.

Using Simpson's rule, the integral within each subinterval is given by:

∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]

where x₀, x₁, and x₂ are the data points within each subinterval.

For the first subinterval [2, 2.2]:

∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]

≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]

For the second subinterval [2.2, 2.4]:

∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]

≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]

Step 3: Sum up the approximations.

To obtain the approximation of the total integral, we sum up the approximations within each subinterval.

Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)

Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.

To learn more about Simpson's rule click here:

brainly.com/question/30459578

#SPJ11

Answer: y+5 = 9/8(x-9)

Step-by-step explanation: Point-slope form is written in y-y1 = m(x-x1) so when you put in (9,-5) in the y1 and x1 spots and substitute the slope 9/8 in for m you get the point-slope form.

Answer:

\(y+5=\frac{9}{8}(x-9)\)

Step-by-step explanation:

Point slope form is: \(y-y_1=m(x-x_1)\)

'm' - slope

(x1, y1) - point

We are given the slope of 9/8 and the point of (9, -5).

Replace 'm', 'x1', and 'y1' with the appropriate values.

\(y-y_1=m(x-x_1)\rightarrow\boxed{y+5=\frac{9}{8}(x-9)}\)

Alternative hypothesis may be one-sided or two-sided.

b) alternative hypothesis.

In statistical hypothesis testing, the alternative hypothesis is one of the suggested propositions in the hypothesis test. In general, the purpose of a hypothesis test is to demonstrate that, under the given conditions, there is sufficient evidence to support the believability of an alternate hypothesis rather than the test's exclusive statement (null hypothesis). Because it is based on a review of the literature and previous studies, it is usually congruent with the research hypothesis. However, the research hypothesis is sometimes congruent with the null hypothesis.

In statistics, alternative hypotheses are frequently denoted as Hₐ or H₁. In a statistical hypothesis test, hypotheses are developed to be compared.

In the field of inferential statistics, two competing hypotheses can be compared using explanatory and predictive power.

This is the two tailed test .

alternative hypothesis is ,

Hₐ :μ≠

For the left tail is

Hₐ : μ<

For the right tail is

Hₐ :  μ >

To know more about alternative hypothesis, visit:

https://brainly.com/question/27335001

#SPJ4

The complete question is :

"In hypothesis testing, which hypothesis can be either one-sided or two sided?

Group of answer choices

a.) null hypothesis

b.) alternative hypothesis"

An example of a +f(pxq) with integer coefficients that factors (poly mod nq), but has no roots is (x^2 + 1)(x^2 + 2). This polynomial satisfies the given conditions and demonstrates that it is possible to have a polynomial with integer coefficients that factors modulo n, but has no roots.

Let's consider the polynomial f(pxq) = (x^2 + 1)(x^2 + 2).
1. This polynomial has integer coefficients as both factors have integer coefficients.
2. Now, let's consider taking the modulo n, where n is any positive integer.
3. Since the modulo operation only affects the coefficients, we will still have a polynomial with integer coefficients after taking the modulo.
4. However, there are no integers x for which f(pxq) = 0 (poly mod n), as the factors x^2 + 1 and x^2 + 2 do not have any integer roots.

To know more about modulo operation visit:

https://brainly.com/question/30264682

#SPJ11

To finf this, we simply divide 25.5 by 51, and then multiply the result by 100.

This is done as follows:

Therefore 25.5 is 50% of 51

If Caroline has 6.8 L of lemonade to serve 20 people. Caroline can pour 340 milliliters of lemonade into each glass.

To find out how many milliliters of lemonade Caroline can pour into each glass, we need to convert the volume of lemonade from liters to milliliters and then divide it equally among the 20 guests.

1 liter is equal to 1000 milliliters. So, Caroline has 6.8 L * 1000 mL/L = 6800 mL of lemonade.

To divide it equally among 20 guests, we divide the total volume of lemonade by the number of guests:

6800 mL / 20 = 340 mL.

Therefore, Caroline can pour 340 milliliters of lemonade into each glass.

Learn more about volume at https://brainly.com/question/11854151

#SPJ11

The line integral along the given curve is -117π/4.

The line integral along the given positively oriented curve can be evaluated using Green's theorem. Let's first find the curl of the vector field F = \(({xe}^{ - 3x} , x^4 + 2x^2y^2)\)\(F/x = 4x^3 + 4xy^2\)\(F/y = 2x^2y^2\)

Taking the difference of these partial derivatives, we get: curl F =\(F/x - F/y = 4x^3 + 4xy^2 - 2x^2y^2\) Now we can use Green's theorem:\(R (4x^3 + 4xy^2 - 2x^2y^2) d\) = ∫C F · dr where R is the region between the circles \(x^2 + y^2 = 9\) and \(x^2 + y^2\)= 16, and C is the boundary of R, which is the positively oriented curve given by \(x^2 + y^2\)= 9 and \(x^2 + y^2\)= 16.

To evaluate the double integral, we can use polar coordinates: θ=0 to 2 r=3 to \(4 (4r^3 cos^3\)+\(4r^3 cos sin^2 - 2r^4 cos sin^2 ) r dr d\)

Simplifying the integrand and evaluating the integral, we get: -117π/4

Learn more about Green's theorem here:

https://brainly.com/question/27549150

#SPJ4

Answer:

C

Step-by-step explanation:

between three and four

The minimum value of the function f(x, y, z) = x^2 - 4x + y^2 - 6y + z^2 - 2z + 5, subject to the constraint x + y + z = 3, is 2.

To find the minimum value of f(x, y, z) subject to the constraint x + y + z = 3, we introduce a Lagrange multiplier λ and form the Lagrangian function L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z) - 3), where g(x, y, z) represents the constraint equation.

Taking partial derivatives of L with respect to x, y, z, and λ, we obtain:

∂L/∂x = 2x - 4 - λ

∂L/∂y = 2y - 6 - λ

∂L/∂z = 2z - 2 - λ

∂L/∂λ = -(x + y + z - 3)

Setting these derivatives equal to zero, we solve the system of equations:

2x - 4 - λ = 0

2y - 6 - λ = 0

2z - 2 - λ = 0

x + y + z - 3 = 0

From the first three equations, we can rewrite λ in terms of x, y, and z:

λ = 2x - 4 = 2y - 6 = 2z - 2

Substituting λ back into the constraint equation, we get:

2x - 4 + 2y - 6 + 2z - 2 = 3

2x + 2y + 2z = 15

x + y + z = 7.5

Now, solving this system of equations, we find x = 2, y = 2, z = 3, and λ = 0. Substituting these values into f(x, y, z), we get f(2, 2, 3) = 2.

Therefore, the minimum value of the function f(x, y, z) = x^2 - 4x + y^2 - 6y + z^2 - 2z + 5, subject to the constraint x + y + z = 3, is 2.

To learn more about function click here, brainly.com/question/30721594

#SPJ11

Answer:

\(\frac{45}{47m^3}\)

Step-by-step explanation:

Given the following question:

\(\frac{45m^2}{47m^5}\)

In order to simplify fractions with exponents we simply subtract the exponents.

\(\frac{45m^2}{47m^5}\)
\(5-2=3\)
\(\frac{45}{47m^3}\)

Hope this helps.

The CDF of X for a constant parameter a > 0, a rayleigh random variable x is \(F_{X}(x) = 1 - e^{(-a^2x^2/2)\) for x > 0, and 0 otherwise.

To find the CDF (Cumulative Distribution Function) of a Rayleigh random variable X with the given \(PDF f_X(x) = {a^2xe^{(-a^2x^2/2)\) for x > 0, 0 otherwise}, we need to integrate the PDF from 0 to x. Here's the solution:

\(CDF F_X(x)\) = ∫\([a^2xe^{(-a^2x^2/2)]}dx\) from 0 to x

Let's denote u = \(a^2x^2/2\). Then, du = \(a^2xdx\). So the integral becomes:

\(F_X(x)\) = ∫\([e^{(-u)}du]\) from 0 to \(a^2x^2/2\)

Now, integrate \(e^{(-u)}\) with respect to u:

\(F_X(x)\) = \(-e^{(-u)\) | from 0 to \(a^2x^2/2\)

Evaluate the definite integral:

\(F_X(x)\) = \(-e^{(-a^2x^2/2)} + e^{(0)} = 1 - e^{(-a^2x^2/2)\)

Thus, the CDF of X is \(F_X(x)\) = \(1 - e^{(-a^2x^2/2)\) for x > 0, and 0 otherwise.

For more such questions on CDF.

https://brainly.com/question/30697050#

#SPJ11

Answer:

3x² – 5x + 2 is a polynomial because:

Exponents are whole numbers, and the expression has at least 1 term.

Exponents other than whole numbers can take the form of variables in denominators, and roots which we don't want.

Answer:

tbh idek im sorry

Step-by-step explanation:

Answer:

\(\displaystyle m=\frac{-2}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph

Point (-3, 1)

Point (3, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer: To verify Mr Ngobeni's statement, we need to calculate his total deductions as a percentage of his net salary and compare it to 25%.

Let's assume Mr Ngobeni's net salary is R10,000.

If his deductions are R2,000, then his total deductions as a percentage of his net salary is:

(2000/10000) x 100% = 20%

Since 20% is less than 25%, Mr Ngobeni's statement is valid.

If his deductions were higher, say R3,000, then his total deductions as a percentage of his net salary would be:

(3000/10000) x 100% = 30%

Since 30% is greater than 25%, Mr Ngobeni's statement would not be valid in this case.