10 is greater than or equal to four minus one.
In symbols, this statement is?

Tiffany didn't deposit any more money and didn't withdraw any,

her balance is $1,413.82.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P(1 + r/n\()^{nt}\)

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Tiffany makes some extra money selling vinyl's to teachers.

She deposited the $1,245 extra money into an account that earned 3.7% interest that was compounded annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.7/100

r = 0.037 rate per year,

Then solve the equation for A

A = P(1 + r/n\()^{nt}\)

A = 1,245.00(1 + 0.037\()^{3.5}\)

A = $1,413.82

Therefore, the amount is $1,413.82.

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Answer:

-30c

Step-by-step explanation:

now:-25

noon - 10pm +10 (got 10c hotter)

-25c-10=-35c(opposite of rise)

midnight - noon: -5c

so do the opposite which is +5

-35+5=-30c

To find one machine that does not work, you expected to buy 200 machines on average.

One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.

A company named Batco sells batteries.

And Batco claims that  99.5% of their batteries are in working order.

That means, 100 - 99.5 = 0.5% of their machines have defect.

0.5 as a fraction of 100% is 0.005.

To find the one machine that does not work;

Divide 1 by fraction of machines not working,

1 / 0.005

= 200

Therefore, you need to buy 200 machines.

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We have to calculate the EAC for both the conveyor belt system.

Solutions :

Equivalent Annual Cost or (EAC) for the SYSTEM-A

\($\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $\)tax rate )

                                \($=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$\)

                               \($= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$\)

                               = $ 49,350

Year      Annual Cost flow     Present value factor    Present Value of Annual

                                                     at 10%                              cash flow

1                    -49,350                  0.909091                          -44,863.64

2                  -49,350                   0.826446                          -40,785.12

3                   -49,350                  0.751315                            -37,077.39

4                   -49,350                 0.683013                         -33,706.71  

     Total                                    $ 3.169865                       $ -156,432.86  

Therefore, Net Present value = present value of the annual cash flow - initial investment.

           = 156,432.86 - 280,000

          = $ 436,432.86 (negative)

Now the EAC or the Equivalent Annual Cost for System A :

\($\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$\)

        \($=\frac{436,432.86}{3.169865}$\)

        \($= 137,681.86 $\) dollar (negative)

\($\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $\)tax rate)

\($=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$\)

\($=(-78,000 \times 0.77)+(60,000 \times 0.23)$\)

= -$ 47,030

Year      Annual Cost flow     Present value factor    Present Value of Annual

                                                     at 10%                              cash flow

1                    -47,030                  0.909091                          -42,754.55

2                  -47,030                   0.826446                          -38,867.77

3                   -47,030                  0.751315                           -35,334.34

4                   -47,030                 0.683013                            -32,122.12

5                  -47,030                  0.620921                            -29,201.93

6                  -47,030                 0.564474                            -26,547.21  

    Total                                     $ 4.355261                       $  -204,827.91

Net Present Value = Present Value of annual cash inflows – Initial Investment

\($= 204,827.91 - 360,000$\)

= -$ 564,827.91 (negative)

EAC for system B:

Equivalent Annual Cost for system B \($=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$\)

\($=\frac{-564,827.91}{4.355261}$\)

= -$129,688.66 (negative)

Answer:

(# - 5) x 2

or

(# - 5) 2

I think it should look Iike this but I might be wrong.

(b) An equilateral triangle has 3-fold rotational symmetry, while (d) A cube has 4-fold rotational symmetry.

Rotational symmetry refers to the property of an object where it looks the same after it has been rotated a certain number of degrees around a central point. The number of times an object looks the same after a full rotation is called its order of rotational symmetry.
(a) An isosceles triangle has no rotational symmetry because it will not look the same after any degree of rotation around its center.

An isosceles triangle has no rotational symmetry. This is because it will not look the same after any degree of rotation around its center. For example, if you rotate an isosceles triangle by 180 degrees, it will be upside down and look completely different.
An equilateral triangle has 3-fold rotational symmetry. This means that it will look the same after being rotated 120 degrees and 240 degrees around its center. To see this, imagine drawing an equilateral triangle and marking its center. If you rotate the triangle 120 degrees around the center, each vertex will be in the same position as before, and the triangle will look the same. Similarly, if you rotate it 240 degrees, it will look the same as the original triangle.

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11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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Answer:

3 feet

Step-by-step explanation:

Lara has 2 pieces of string. One is 15 feet long and the other is 12.

We solve this question using the Greatest Common Factor method.

We have to find the factors of 12 and 15

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3.

Therefore, the greatest length, in feet, that she can make is 3 feet

Answer:

10

Step-by-step explanation:

the small engine tanks that Harvey have = 5 ÷ ½ = 10

Answer:

(4)+9= P+ (13)

Step-by-step explanation:

Since 13=13, we have proven the Associative Property of Addition using the numbers a=P, b=4, and c=9

The additive rate of change is true of the data set if a linear function can be used to represent the data

When we have dependent and independent variables we will have a linear relationship.

Let x be the independent variable and y be the dependent variable.

To write the  relationship we will have :

y = kx + c

Where k and c are constants.

In the case of a line, the constant k is the gradient.

A multiplicative change is a log form and it is given by :

Y = Ck^x

The relationship is not linear but exponential.

The correct answer is thus: Additive rate of change.

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Answer:

55 inches = 4 feet 7 inches

Step-by-step explanation:

As we know 12 inches = 1 feet

so, 55 inches = 55÷12

4 feet 7 inches

Answer:

55 inches=4 feet 7 inches

Hope it helps

to factor we must recognize the elements in common

the r exist on both terms, so we can divide by r on each term to factor

The difference of the given function is 245 or 235, depending on how the expression is interpreted.

To find and simplify the difference of the function f(x) = 312 - 72 - 5, we need to perform the arithmetic operations in the given expression.

First, let's simplify the subtraction inside the parentheses:

72 - 5 = 67

Now, we can substitute this simplified value back into the expression:

f(x) = 312 - 67

Next, we perform the subtraction:

312 - 67 = 245

Therefore, the difference of the function f(x) = 312 - 72 - 5 is 245.

It's important to note that in the given expression, there seems to be a redundancy in the subtraction operation. The expression "312 - 72 - 5" is equivalent to "312 - (72 + 5)" since subtraction is associative. Therefore, the simplified expression would be "312 - 77", which results in the same value of 235.

In summary, the difference of the given function is 245 or 235, depending on how the expression is interpreted.

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The value of x in the figure, using the cases is solved to be

The values of x is solved in three cases

Case 1: Linear pair of 2x be z

Here z = 180 - 2x

Case 2: Linear pair of 4x be y

Here y = 180 - 4x

Case 3: In the triangle

Here x + y + z = 180

plugging in the values

x + 180 - 4x + 180 - 2x = 180

collecting like terms

x - 4x - 2x = 180 - 180 - 180

-5x = -180

x = 36

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The most specific name for the figure is an isosceles trapezoid

From the question, we have the following parameters that can be used in our computation:

The figure

The properties of the given figure are

Using the above as a guide, we have the following:

The figure is a trapezoid

Because the nonparallel sides are congruent, then the most specific name for the figure is an isosceles trapezoid

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1.The formula for g(x), the graph of f(x) shifted up 3 units and left 2 units, is g(x) = 3√(x + 2) + 3.

2.After performing the transformations of shifting upward 96 units and shifting 85 units, the new function is f(x) = (x + 85)² + 96.

To shift the graph of f(x) up 3 units, we add 3 to the original function. Additionally, to shift it left 2 units, we subtract 2 from the variable x. Therefore, the formula for g(x) is g(x) = 3√(x + 2) + 3.

Given the function f(x) = x², to shift it upward 96 units, we add 96 to the original function. Similarly, to shift it 85 units to the right, we subtract 85 from the variable x. Thus, the transformed function is f(x) = (x + 85)² + 96. This means that for any given value of x, we square it, then add 85, and finally add 96 to obtain the corresponding y-value on the transformed graph.

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9514 1404 393

Answer:

Step-by-step explanation:

Horizontally the table values total the number in the first column.

  first row missing table value = 700 -665 = 35

  second row missing table values = 300 -240 = 60

__

The conditional probability formula applies.

  P(contains | positive) = P(contains & positive)/P(positive)

The probability associated with each table entry is that value divided by 1000. Then the numbers in the formula are ...

  P(contains | positive) = .665/(.665+.060) = .665/.725 ≈ 91.7%

\(\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}\star\)

35

3591.7

3591.760

Step-by-step explanation:

Horizontally the table values total the

number in the first column.

first row missing table value = 700-665

second row missing table values = 300

-240 60

35

The conditional probability formula

applies.

P(contains I positive) = P(contains &

positive)/P(positive)

The probability associated with each

table entry is that value divided by 1000.

Then the numbers in the formula are ..

.665/.725 91.7%

P(contains I positive) = 665/(665+.060)

Answer:

Since the full percentage of something is 100% thats because 1*100 = 100.

So since it has 40% chance of rain what would 100-40 be? Well it would be 60. So the probability that it will not rain is

Answer:

(2, - 5 )

Step-by-step explanation:

Given the 2 equations

y = - 3x + 1 → (1)

4x + y = 3 → (2)

Substitute y = - 3x + 1 into (2)

4x - 3x + 1 = 3

x + 1 = 3 ( subtract 1 from both sides )

x = 2

Substitute x = 2 into (1) for corresponding value of y

y = - 3(2) + 1 = - 6 + 1 = - 5

solution is (2, - 5 )

Using the z table, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

In the given question,

We have to find the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82%.

The confidence interval is 82%.

We can write 82% as 82/100 and 0.82.

Now the value of

\(\alpha\)=1−0.82

\(\alpha\)=0.18

Now finding the value of \(\alpha\)/2

\(\alpha\)/2=0.18/2

\(\alpha\)/2=0.09

Now finding the value of \(z_{a/2}\).

\(z_{0.82}\) = 1.34

Hence, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

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Answer:

y = 1/2x + 4

Step-by-step explanation:

The slope intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-2,3) (2,5)

We see the y increase by 2 and the x increase by 4, so the slope is

m = 2/4 = 1/2

The y-intercept located at (0,4)

So, the equation is y = 1/2x + 4

The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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When U = 10, the value of n is 112.604.

We are given that the number n is the algebraic sum of two terms:

Term 1 varies directly as u.

Term 2 varies inversely as U².

Let's denote the first term as k1 u, where k1 is the constant of proportionality.

And let's denote the second term as k2/U², where k2 is another constant of proportionality.

We have,

When U = 2, n = 22.

When U = 8, n = 56.5.

So, Equation 1: n = k1u + k2/U²

Equation 2: 22 = k1(2) + k2/(2)²

Equation 3: 56.5 = k1(8) + k2/(8)²

Let's solve these equations to find the values of k1 and k2.

Equation 2 becomes: 22 = 2k1 + k2/4

Equation 3 becomes: 56.5 = 8k1 + k2/64

To eliminate k2, let's multiply Equation 2 by 64:

1408 = 128k1 + k2

Now we have two equations with two variables:

128k1 + k2 = 1408

8k1 + k2/64 = 56.5

Let's subtract Equation

120k1 = 1351.5

k1 = 1351.5 / 120

k1 = 11.2625

Substituting the value of k1 back into Equation 2:

22 = 2(11.2625) + k2/4

22 = 22.525 + k2/4

k2/4 = 22 - 22.525

k2/4 = -0.525

k2 = -2.1

Now we have the values of k1 and k2:

k1 = 11.2625

k2 = -2.1

Finally, we can find the value of n when U = 10 by substituting these values into Equation 1:

n = k1u + k2/U²

n = 11.2625(10) - 2.1/(10)²

n = 112.625 - 2.1/100

n = 112.625 - 0.021

n ≈ 112.604

Therefore, when U = 10, the value of n is 112.604.

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The smallest p-value is always associated with the z-score that is furthest away from the mean. This is because the tails of the normal distribution curve have less area and thus represent smaller p-values. The correct answer is option (d) z = -3.24.

In a hypothesis test, there are two hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1).

The null hypothesis is the one we're testing, while the alternative hypothesis is the one we're trying to support or prove.

A two-tailed alternative hypothesis is one in which we are interested in whether a parameter is not equal to a certain value, as opposed to one-tailed alternative hypotheses, in which we are interested in whether the parameter is greater than or less than a certain value.

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Answer:

x =-35

Step-by-step explanation:

2/5x−3=−17

Add 3 to each side

2/5x−3+3=−17+3

2/5x = -14

Multiply each side by 5/2

5/2 * 2/5x = -14 * 5/2

x = -35

Answer:

x = -35

Step-by-step explanation:

I hope this helps!

Answer:

Han forgot to divide -10x by 4

Step-by-step explanation:

Han made a mistake when isolating y in the slope intercept equation.

When dividing both sides by 4, he only divided 20 by 4, and forgot to divide -10x by 4.

The equation in slope intercept form should have been y = -2.5x + 5

Using this, the x intercept should have been (2, 0) instead. He got the y intercept right, which is (0, 5)

So, the mistake he made was forgetting to divide -10x by 4

The error in the calculation made is that Han did not divide 10x by 4 to Obtain the correct slope - intercept relation :

From ; 4y = 20 - 10x

Divide both sides by 4 to isolate y :

y = 5 - 2.5x

Hence, the slope intercept equation is y = 5 - 2.5x

X - intercept :

Value of x ; when y = 0

0 = 5 - 2.5x

2.5x = 5

x = 5 / 2.5

x = 2

Hence, intercept = (2, 0)

Y - intercept :

Value of y when x = 0

y = 5 - 2.5(0)

y = 5 - 0

y = 5

y - intercept = (0, 5)

Therefore, the error made is failing to divide 10 by 4 in the slope intercept equation.

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There are 22 people who sent the chain letter, and 189 people did not continue the chain.

We know that the chain started with one person who sent it to 7 others, so that makes a total of 8 people in the first round. In the second round, each of those 7 people could either send it to 7 more people or ignore it, so there are two possibilities for each of those 7 people: they either continue the chain or they don't.

Therefore, there are 2⁷ = 128 possible outcomes for the second round.

If we assume that everyone who received the letter in the second round sent it to 7 more people, then there would be 7 x 128 = 896 people in the third round.

Continuing this pattern, we can see that the number of people in each round is given by the formula of combination 8 x 7ⁿ⁻¹, where n is the round number (starting with n = 1 for the first round).

We want to find the round number such that the total number of people in the chain is 211. Setting the formula above equal to 211 and solving for n gives

8 x 7ⁿ⁻¹ = 211

7ⁿ⁻¹ = 26.375

n - 1 = log_7(26.375)

n = 2.78 (rounded to two decimal places)

Since we can't have a fractional round number, we can assume that the chain ended after the second round (since the third round would have too many people). Therefore, the total number of people who sent the letter is

8 + 7(2) = 22

To find the number of people who did not continue the chain, we can subtract the number of people who sent the letter from the total number of people in the chain

211 - 22 = 189

Therefore, 189 people did not continue the chain.

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Answer:

x < --8

Step-by-step explanation:

i hope this helps im a little rusty on math (:

Answer:

x < - 8

Step-by-step explanation:

\(\frac{3}{4}\) x + 7 < 1 ( subtract 7 from both sides )

\(\frac{3}{4}\) x < - 6 ( multiply both sides by 4 to clear the fraction )

3x < - 24 ( divide both sides by 3 )

x < - 8

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)