A certain sum is invested at 4% annual interest. If $1400 is added to the account, the annual interest will amount to $196. How much was originally invested?

Answer:

15

Step-by-step explanation:

To find the common denominators for 2/3 and 1/5, just look at the denominators for both of the fractions, 3 and 5

Multiply 3 and 5, which is 15. 15 is the common denominator.

904.32 inches²

Explanation:

diameter = 12 inches

diameter = 2(radius)

radius = diameter/2 = 12/2

radius = 6 inches

height = 8 inches

let π = 3.14

The formula for volume of a cylinder:

To the nearest hundredth, volume of cylinder is 904.32 inches²

The rate at which the height of the water is increasing when water is being pumped in at a rate of 2/3 m/s and the water is 9m deep is 0.667 m/s.

We can start by using the formula for the volume of a square pyramid to find the volume of water in the tank. Let V be the volume of water in the tank and h be the height of the water.

V = (s² [h])/3

We know that the base of the pyramid is 3m by 3m, so s = 3. Also, the height of the pyramid is 16m, so we have:

V = (3² [h])/3

V = 3h

Now, we can find the rate of change of the volume with respect to time:

dV/dt = 3 [dh/dt]

We know that water is being pumped in at a rate of 2/3 m/s, so dh/dt = 2/3. We want to find how fast the height increases when the water is 9m deep, so h = 9. Substituting these values, we get:

dV/dt = 3 [dh/dt]

dV/dt = 3 [2/3]

dV/dt = 2

Therefore, the rate at which the volume of water is increasing is 2 cubic meters per second. To find the rate at which the height of the water is increasing, we need to solve for dh/dt:

dV/dt = 3 [dh/dt]

2 = 3 * dh/dt

dh/dt = 2/3

So the height of the water is increasing at a rate of 2/3 m/s when the water is 9m deep. Rounded to 3 decimal places, the answer is 0.667 m/s.

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A key problem faced by poorer inner-city neighborhoods in America due to their geographical position is a lack of quality food options.

One of the significant challenges faced by poorer inner-city neighborhoods in America is the limited availability of quality food options, commonly referred to as "food deserts." Food deserts are areas where residents have limited access to fresh, nutritious, and affordable food. These neighborhoods often lack grocery stores, farmers markets, and other sources of healthy food, leaving residents with few choices but to rely on convenience stores and fast food outlets that predominantly offer processed and unhealthy food options.

The geographical positioning of these neighborhoods plays a crucial role in this interest. Many low-income inner-city neighborhoods are located in areas that are underserved by grocery stores and supermarkets.

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The correct answers are: Grams of iron in a meal, Minutes spent on this test, Snacks eaten in a week

Parametric statistics could be used to analyze the following dependent variables:

Grams of iron in a meal: Parametric statistics can be used to analyze continuous numerical variables, such as the amount of iron in a meal, by assuming a specific distribution (e.g., normal distribution) and using techniques like t-tests, ANOVA, or regression.

Minutes spent on this test: Similarly, parametric statistics can be applied to analyze continuous numerical variables like the time spent on a test. Techniques such as t-tests or regression can be used to compare groups or explore relationships between variables.

Snacks eaten in a week: Parametric statistics can also be used for analyzing count data, such as the number of snacks eaten in a week. Techniques like Poisson regression or negative binomial regression can be used to model and analyze count data.

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V is the set of polynomials of the form a + bx, V is a vector space over the field of scalars, and it satisfies all the given properties.

Let V be the set of polynomials of the form a + bx, where a and b are scalars. We can show that V is a vector space over the field of scalars using the given operations and properties.

Closure under addition: Let u and v be objects in V. Then u = a1 + b1x and v = a2 + b2x for some scalars a1, b1, a2, and b2. The sum u + v is defined as (a1 + a2) + (b1 + b2)x, which is also of the form a + bx. Therefore, u + v is in V.

Commutativity of addition: u + v = (a1 + a2) + (b1 + b2)x = (a2 + a1) + (b2 + b1)x = v + u.

Associativity of addition: u + (v + w) = (a1 + a2) + (b1 + b2)x + (a3 + b3x) = (a1 + (a2 + a3)) + (b1 + (b2 + b3))x = (u + v) + w.

Existence of a zero vector: Let 0 be the polynomial 0 + 0x. Then for any u in V, we have 0 + u = (0 + a) + (0 + b)x = a + bx = u and u + 0 = (a + 0) + (b + 0)x = a + bx = u.

Existence of additive inverses: Let u = a + bx be an object in V. Then the negative of u is -u = -a - bx. We have u + (-u) = (a + bx) + (-a - bx) = 0 + 0x = 0 and (-u) + u = (-a - bx) + (a + bx) = 0 + 0x = 0.

Closure under scalar multiplication: Let k be any scalar and u = a + bx be any object in V. Then ku = ka + kbx is also of the form a + bx. Therefore, ku is in V.

Distributivity of scalar multiplication over vector addition: k(u + v) = k((a1 + b1x) + (a2 + b2x)) = k((a1 + a2) + (b1 + b2)x) = ka1 + ka2 + kb1x + kb2x = (ka1 + kb1x) + (ka2 + kb2x) = ku + kv.

Distributivity of scalar multiplication over scalar addition: (k + m)u = ((k + m)a) + ((k + m)bx) = (ka + ma) + (kb + mb)x = (ka + kb)x + (ma + mb)x = ku + mu.

Associativity of scalar multiplication: k(mu) = k(ma + mbx) = km(a + bx) = (km)a + (km)bx = (km)u.

The identity element of scalar multiplication: 1u = 1(a + bx) = a + bx = u.

Therefore, V is a vector space over the field of scalars, and it satisfies all the given properties.

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Answer: 3ab   IF a^b does NOT mean a to the power of b!

I believe you mean  9a²b and 30ab³

If you really mean 9aᵇ and 30ab³,  then the GCF is 3a.

Step-by-step explanation:

the factors of  9 are 3*3  The factors of 30 are 2*3*5.

The only common factor of 9 and 30  is 3

a is a common factor of a and a²

b is a common factor of b and b³

System of Equations

Let

x = Number of laptops

y = Number of tablets

There are 30 salespeople and the business wants to assign one device to each one of them, thus:

x + y = 30

Each laptop cost $515 and each tablet cost $285. The business has $11,080 to spend in the new equipment, thus:

515x + 285y = 11,080

The system of equations that models the problem is:

x + y = 30

515x + 285y = 11,080

The exact length of the curve is approximately equal to 1.078 units.

To obtain the length of the curve, we are to integrate the function's derivative that is the square root of the sum of the squares of the first derivative and 1.

Hence we begin by finding the derivative of the given equation:

y = x³/3 + (1/4)xdy/dx = d/dx(x³/3 + (1/4)x)dy/dx = x² + (1/4)

The derivative of the equation is dy/dx = x² + 1/4

Now we can find the length of the curve by integrating the square root of the sum of the squares of the first derivative and 1.

Hence we obtain that:

L = ∫₁³√[(1 + dy/dx²)]dxL = ∫₁³√[(1 + (x² + 1/4)²)]dx

We can evaluate the indefinite integral of the above equation by letting u = x² + 1/4 so that du/dx = 2x.

Then we obtain:

du/dx = 2x ==> dx = du/2x

Thus the integral equation becomes:

L = ∫₁³√[1 + u²] du/2x

On integrating using the formula for the inverse hyperbolic tangent we obtain:

L = (1/2)∫₁³√1/u² + 1 du= (1/2)[arctanh(u)]₄₁= (1/2)[arctanh(16/13) - arctanh(5/4)]= (1/2)[2.351∣∣−0.804]= 1.078 units (approx)

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Answer:

$21,000

Step-by-step explanation:

(refer to attached for reference)

Assuming simple interest, the applicable formula is

A = P(1 + rt)

Where:

A = final amount (we are asked to find this)

P = Principal (Beginning amount) = $15,000

r = annual interest rate = 12% = 0.12  (i'm assuming that we are given annual rate)

t = time = 40 months = 3.333 years

Hence substituting all the above into the equation,

A = P(1 + rt)

A = (15,000) [1 + (0.12)(3.333)]

A = $21,000

Answer:

She lives in the Southern Hemisphere.

Step-by-step explanation:

Answer:

7 1/2 cups

Step-by-step explanation:

If Carol uses 1 1/4 cups of flour for 2 muffins, then she will need to repeat this conversion 6 times since she wants to make identical 12 muffins in all.

So, 1 1/4 * 6 = 7 1/2

Therefore, she needs 7 1/2 cups of flour

Hope that helps! :)

Answer:

umm

Step-by-step explanation:

The number of hours that Julius can spend online this week is 1 1/3 hours.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.

This will be Illustrated as x.

x + 1 2/3 ≤ 3.

x ≤ 3 - 1 2/3

x ≤ 1 1/3.

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We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,(\(H_{0}\)):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,(\(H_{A}\)) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ \(\sqrt{p'(1-p')/n}\) ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ \(\sqrt{0.231( 1- 0.231)/ 273}\)

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

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The first option in the second row, Option(C) represents the data.

In order to solve the problem,

First, we need to arrange the numbers in ascending order.

4, 7, 8, 10, 11, 13, 15, 15, 22, 28

Median = 11+13/2

            = 12

From the first range ( 4,7,8,10,11 ) , we can find Q1 also known as first quartile where Q1 = 8 ( middle-most number).

Similarly, from the second range ( 13,15,15,22,28 ) , we can find Q2 also known as third quartile where Q3 = 15 (middle-most number ).

Now, for the box plot,

We need to draw a number line from 0 to 32.

Next, we need to draw a box from Q1 to Q3 with a vertical line through the median.

Next, we put dots above 4 and 28 since our numbers start from 4 and end with 28.

Finally we join the dots and the box plot with a straight line.

Hence, option C is the correct choice.

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Answer:

454

Step-by-step explanation:

need 800 in 5 years

x*(1+12%)^5 = 800

so 1.76x=800

x=454

Answer:

Step-by-step explanation:

The missing factor has the form (x - a).  The given factor is (x - 7).  The product (a)(-7) must be -42, and therefore the missing factor is (x + 6)

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Weighted Mean = (90 × 25% + 79 × 20% + 82 × 10% + 70 × 15% + 85 × 15%) / (25% + 20% + 10% + 15% + 15%)

Unweighted Mean = (90 + 79 + 82 + 70 + 85) / 5

One student, Kyle, hasn't taken his final exam yet, but his marks in the first five categories are 90, 79, 82, 70, and 85. This problem requires determining the weighted mean for Kyle before the final exam and comparing it to the unweighted mean.

To calculate the weighted mean for Kyle before the final exam, we need to multiply each category's mark by its corresponding weight, sum them up, and divide by the total weight. For Kyle, the weighted mean would be calculated as follows:

Weighted Mean = (Knowledge × 25% + Application × 20% + Thinking × 10% + Culminating Project × 15% + Final Exam × 15% + Communication × 15%) / (Total Weight)

However, since Kyle hasn't written his final exam yet, we can exclude the Final Exam mark and its weight from the calculation. The weighted mean would then be:

Weighted Mean = (90 × 25% + 79 × 20% + 82 × 10% + 70 × 15% + 85 × 15%) / (25% + 20% + 10% + 15% + 15%)

To find the difference between the weighted mean and the unweighted mean, we need to calculate the unweighted mean by simply taking the average of the marks in the first five categories:

Unweighted Mean = (90 + 79 + 82 + 70 + 85) / 5

By comparing the weighted mean and the unweighted mean, we can evaluate how much the inclusion of weights for different categories affects Kyle's overall mark.

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Therefore, the sample size for each group should be 139 in order to meet the guideline.

The formula for standard error is the standard deviation of the sample divided by the square root of the sample size. The formula for the estimated difference between means is the difference between the two means.

Given the researcher anticipates that the means of the two groups will differ by about 1 inch and that in each group the standard deviation of plant growth will be around 1.5 inches.

The following conditions must be satisfied for the anticipated SE for each experimental group to be no more than one-fourth of the anticipated difference between the two group means:n = [(Zc x s) / E]^2Where: n = sample sizeZc = the critical value (the critical value for a 95% confidence level is 1.96)s = the estimated standard deviation (1.5 inches in this case)E = the anticipated SE (0.25 x 1 inch = 0.25 inches)Putting the values into the formula;n

\(= [(1.96 x 1.5) / 0.25]^2= (2.94 / 0.25)^2= 11.76^2= 138.18\)

The sample size for each group should be 138.18 or 139 to meet the guideline.

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Answer:

x = -3

Step-by-step explanation:

5x + 45 = 30

     - 45  - 45

5x = -15

5        5

x = -3    

Answer: The tree house is 8 feet off the ground, or 96 inches up because (8)(12) = 96. Each knot needs 2 extra inches, so the expression for the length of rope needed is 96 + 2n. If n = 8, then Peter will need 96 + 2(8) = 112 inches of rope.

Step-by-step explanation: plz mark brainiest

The rope is anchored 5.3 feet from the tree

Represent the required distance with x

Using the Pythagoras theorem, we have:

8^2 = 6^2 + x^2

Evaluate the squares

64 = 36 + x^2

Evaluate the like terms

x^2 = 28

Take the square of both sides

x = 5.3

Hence, the rope is anchored 5.3 feet from the tree

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And then write:

Y(s) = (-4X(s))/s

Let's take a step-by-step approach to solving this problem.

First, we are given the differential equation:

y'' + 4y = 0

To solve this using Laplace transforms, we take the Laplace transform of both sides:

L{y'' + 4y} = L{0}

Using the linearity property of the Laplace transform and the fact that L{y''} = s^2Y(s) - s*y(0) - y'(0), we can simplify this to:

s^2Y(s) - s*y(0) - y'(0) + 4Y(s) = 0

Next, we solve for Y(s):

Y(s)(s^2 + 4) = s*y(0) + y'(0)

Y(s) = (s*y(0) + y'(0))/(s^2 + 4)

To find the partial fraction decomposition of Y(s), we factor the denominator:

s^2 + 4 = (s + 2i)(s - 2i)

And then use partial fractions to write:

Y(s) = (a/(s + 2i)) + (b/(s - 2i))

To solve for a and b, we multiply both sides by the denominators:

Y(s)(s + 2i)(s - 2i) = a(s - 2i) + b(s + 2i)

And then substitute s = -2i and s = 2i to get two equations:

a(-4i) = -2iy(0) + y'(0) - b(4i)

a(4i) = 2iy(0) + y'(0) + b(4i)

Solving for a and b, we get:

a = (y(0) + 2iy'(0))/(4i)

b = (y(0) - 2iy'(0))/(4i)

Now, we can write the partial fraction decomposition of Y(s):

Y(s) = ((y(0) + 2iy'(0))/(4i))/ (s + 2i) + ((y(0) - 2iy'(0))/(4i))/(s - 2i)

To find y(t), we need to take the inverse Laplace transform of Y(s). We can use the partial fraction decomposition to do this:

y(t) = (1/2)*(y(0)cos(2t) + (y'(0)/2)sin(2t))

Now, we move on to the second part of the problem, which is to use Laplace transforms to solve the initial value problem:

x(0) = 0, y(0) = 0

We are given the following system of differential equations:

x' = y

y' + 4x = 0

Taking the Laplace transform of both equations, we get:

sX(s) = Y(s)

sY(s) + 4X(s) = 0

Solving for Y(s) and X(s), we get:

Y(s) = X(s)/s

X(s) = -4Y(s)/s

To find the partial fraction decomposition of X(s) and Y(s), we factor the denominators:

sY(s) + 4X(s) = 0

sX(s) = Y(s)

s(sY(s) + 4X(s)) = 0

sX(s) = Y(s)

s^2Y(s) + 4sX(s) = 0

sX(s) = Y(s)

And then write:

Y(s) = (-4X(s))/s

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Answer:

Step-by-step explanation:

Let the number of notes is x.

20% of notes is:

40% of the remainder is:

Remaining notes are:

Total of the notes:

We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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In Algebra, when representing data on two quantitative variables, you can create a scatter plot to visually display the relationship between these variables. The scatter plot consists of points that represent individual data points, with one variable on the x-axis and the other on the y-axis.

In algebra, one important skill is being able to represent data on a scatter plot. This involves plotting two quantitative variables and visually analyzing how they are related.

The variables can be any numerical data points such as height and weight, age and income, or any other pair of quantitative measurements.

By analyzing the scatter plot, we can determine whether the variables have a positive or negative correlation, or whether they are independent of each other.

Understanding how to represent data on a scatter plot and analyzing the relationship between variables is an essential skill in algebra and in many other fields that use data analysis.

By examining the scatter plot, you can determine if there's a positive, negative, or no correlation between the variables, as well as identify any outliers or trends in the data.

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Answer: burn

Step-by-step explanation: yeah so yeah and so if u do that u get that answer with so yyeah and yeahh

I think ur question is erorr.

hope it hepls u a lot