Evaluate \(8^{10/}\)\(8^{2}\) using the quotient of exponents property.

The number of months that it would take for the price of the gallon to get to 1.90 dollars is 20 months.

We have the following details with which we are to solve this problem.

The price of gas is given as $1.79

The rate of increase is given as 0.3% = 0.003

We are to find the value for when it would be $1.90

The formula that would be used to solve this is given as

\(F = P * (1 + r)^n\)

Where f = final value

p = present value

r = rate

n = number of months

From the question

f = 1.90

p = 1.79

r = 0.03

we have to put these values in the formula that we have here

\(1.9 = 1.79 * (1 + 0.03)^n\)

\(1.9 = 1.79 * (1.003)^n\)

Divide through by 1.79

\(\frac{1.9}{1.79} = (1.003)^n\)

take the ln of both sides

\(ln\frac{1.9}{1.79} = nln(1.003)\)

We have to simplify the equation above from this stage

ln1.0615 = n0.002995

0.05968 = n0.002995

divide through by the value of n

n = 0.05968 / 0.002995

n = 19.92

n ~ 20

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By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.

In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:

(t, h) = (0 s, 5 ft)

Second, the final height of the ball is equal to:

h = 5 ft

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Answer:

33) BD = 5.36

34) x = 67

* Don't forget to put a degree sign with 34)

Step-by-step explanation:

33)

In this problem, it is given that 2 of the sides are congruent, this means that the given triangle, by definition is isosceles. Yet if one adds up the given angle measures;

m< BAC = m<BAD + m<DAE + m<EAC -> Parts whole postulate

m<BAC = 15 + 30 + 15

m<BAC = 60

An isosceles triangle with a 60 angle is an equilateral triangle, therefore, one can say that all the sides and angles are congruent.

BA = AC -> sides equliateral triangle

m<B = m<C -> angles in an equilateral triangle

m<BAD = m<EAC -> given

ΔBAD ≅ ΔEAC -> side-angle-side

Therefore one can say that;

BD = EC ->corresponding parts of congruent triangles are congruent

Hence;

BD + DE + EC = BC

2BD + 9.28 = 20

2BD = 10.72

BD = 5.36

34)

1) m<PQL = y -> naming

2) m<PQL = m<LQN -> definiton of angle bisector

3) m<PQL + m<QLP + m<LPQ = 180 -> sum angles in a triangle

y + 70 + x = 180

x = 110 - y

4) m<PQL + m<LQM = 2y = m<PQM -> parts-whole-postulate

5) m<QLM = 180 - m<LQN + m<M -> sum of angles in a triangle

m<QLM = 126 - y

6) m<QLM + m<PLQ + m<NLP = 180 -> definition of a straight angle

126 + 70 + m<NLP = 180

m<NLP = y - 16

7) ΔPNL - isosceles -> deinfion of isosceles; Pn = NL

8) m<NPL + m<QPL = m<P -> parts-whole posulate

9) m<PQM + m<P = 180 -> two parralell lines intersected by a transversal

(110 - y) + (y - 16) + 2y = 180

94 + 2y = 180

2y = 86

y = 43

10) 110 - y = x -> substitution

110 - 43 = x

67 = x

Cosine formula

Considering angle R, the adjacent side has a length of 9 units, and the hypotenuse of the triangle has a length of 15 units. Substituting this information into the above formula:

Answer:

√115

Step-by-step explanation:

14²= 9² + x²

x= √14²-9² = √115

Step-by-step explanation:

using Pythagores theorem

h²=p²+b²

14²=p²+9²

p²=196-81

p=√115

p=10.72

Answer: D - 5 1/4

Step-by-step explanation:

7/8 x 6 = 5.25

5.25 = 21/4

21/4 = 5 1/4

Answer:

D) 5 1/4

Step-by-step explanation:

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

a) Range is 24 , b) MAD is 8.88 , c) Variance is 126.60 , d) Standard deviation is 11.25.

a. The range is the difference between the largest and smallest values in the data set. The largest value is 50 and the smallest value is 26, so the range is:

50 - 26 = 24

b. MAD stands for Mean Absolute Deviation, which is the average of the absolute differences between each value in the data set and the mean of the data set. To calculate the MAD, first we need to find the mean:

Mean = (40 + 48 + 26 + 50 + 38 + 46) / 6 = 39.67

Next, we find the absolute difference between each value and the mean, and then take the average of those absolute differences:

|40 - 39.67| = 0.67

|48 - 39.67| = 8.33

|26 - 39.67| = 13.67

|50 - 39.67| = 10.33

|38 - 39.67| = 1.67

|46 - 39.67| = 6.33

Average of absolute differences = (0.67 + 8.33 + 13.67 + 10.33 + 1.67 + 6.33) / 6 = 6.89

So the MAD is 6.89.

c. The sample variance measures how spread out the data is by calculating the average of the squared differences between each value in the data set and the mean of the data set. To calculate the sample variance, first we need to find the mean (which we already calculated in part b):

Mean = 39.67

Next, we find the squared difference between each value and the mean, and then take the average of those squared differences:

\((40 - 39.67)^2 = 0.1089\)

\((48 - 39.67)^2 = 75.0089\)

\((26 - 39.67)^2 = 187.4889\)

\((50 - 39.67)^2 = 108.0089\)

\((38 - 39.67)^2 = 2.7889\)

\((46 - 39.67)^2 = 39.3489\)

Average of squared differences = (0.1089 + 75.0089 + 187.4889 + 108.0089 + 2.7889 + 39.3489) / 6 = 66.2567

So the sample variance is 66.26.

d. The sample standard deviation is the square root of the sample variance. So the sample standard deviation is:

\(\sqrt{(66.26)} = 8.13\)  (rounded to 2 decimal places)

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Answer:

the answer will be number two x=+4\(\sqrt 20\)

Step-by-step explanation:

if u can brainliest plsss

Answer:

A. x= ±2√10

Step-by-step explanation:

subtract 40 from each side

divide each side by the negative

take the square root of both sides

simplify the square root of 40

±2√10

The number of points gained overall by Julia playing the game is 30 point

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

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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The new coordinate will be T'(3.2 , -1.6) .

Dilation is the transformation that changes the size of the object without changing its shape .

If a coordinate point is (x,y) and a dilation of scale factor f is applied then the new coordinates will be (fx ,fy)

The coordinate given in the question is T(8, -4)

The scale factor is 0.4

The new coordinate is

T'( 0.4 * 8 , 0.4 * (-4))

T'(3.2 , -1.6)

Therefore the new coordinate will be T'(3.2 , -1.6)

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Answer:

The width is 9 feet and the length is 15 :)

Step-by-step explanation:

rawr

Answer:

The given expression does not define \(y\) as a function of \(x.\) (Answer: No)

Step-by-step explanation:

Let be \(x+9 = y^{2}\), as we have understood from mathematical reading. This function indicates that \(y^{2}\), not \(y\) is a explicit function of \(x\). The correct form is obtained by increasing each side of the formula by \(\frac{1}{2}\), that is to say:

\((x+9)^{\frac{1}{2} } = (y^{2})^{\frac{1}{2} }\)

\(y = \pm \sqrt{x+9}\)

Hence, the given expression does not define \(y\) as a function of \(x.\)

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

in 8 years both school will have 650 students

Step-by-step explanation:

HS A (t) = 250+50t

HSB (t) = 450+25t

250 + 50t = 450 + 25t

25t=200

t=8

in 8 years

to graph this:

HSA points (0,250) (2, 350) (4, 450) (8, 650)(10, 750)

HSB points (0, 450) ( 2, 500) (4, 550) (8, 650) (10, 700)

when you graph then you will notice they intercept at 8, which gives you 650 students

A person who has owned a Roth IRA for five years may withdraw money from the account to buy their first home. The individual has to meet certain requirements and can't withdraw more than $10,000 per person.

A Roth IRA is a type of individual retirement account that allows for tax-free withdrawals of contributions at any time, without penalty or taxes. After five years of ownership, a person who has a Roth IRA may withdraw money from the account to buy their first home. This withdrawal is known as a "first-time homebuyer distribution."

However, there are certain rules and limitations to be aware of when withdrawing money from a Roth IRA for a first home purchase. The individual must be a first-time homebuyer, defined as someone who has not owned a home in the past two years. Additionally, the maximum amount that can be withdrawn for a first home purchase is $10,000 per person.

It's important to note that while contributions to a Roth IRA can be withdrawn tax-free and without penalty, earnings on those contributions may be subject to taxes and penalties if withdrawn before age 59 and a half.

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a ) She takes 2 minutes  = 120 seconds to serve 1 drink .

b ) The range in the amounts donated = 225

c ) The mean amount donated  = $ 83

d ) The print company donated $200 .

She serves 40 drinks  in 20 minutes

⇒ 1 drink = 40/20 = 2 minutes = 2 * 60  = 120 seconds

Therefore , she takes 2 minutes  = 120 seconds to serve 1 drink .

Range in amounts donated = highest value - lowest value

                                             = 250 - 25

                                              = 225

Mean amount donated = Total of value of obs. /No. of obs.

                                        = ( 250 + 25 + 40 + 35 + 65 ) / 5

                                        =  $83

Let the amount print company paid be x .

⇒  ( 250 + 25 + 40 + 35 + 65 + x ) / 6 = 102.50

   ( 250 + 25 + 40 + 35 + 65 + x ) = 615

 x = 200

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Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

The length of a rectangle cannot be negative, hence the length of the rectangle is 7 units.

Based on the question given, the width (W) is the length (L) minus 3 units, which can be expressed as:

W = L - 3

The formula for the area (A) of a rectangle is:

A = Length × Width

We are given that the area is 28 square units, so:

A = 28

Now, we can substitute the expressions for width (W) and area (A) into the area formula:

28 = L × (L - 3)

Now, we need to solve this quadratic equation for L. First, expand the equation:

28 = L^2 - 3L

Now, rearrange the equation in standard quadratic form

L^2 - 3L - 28 = 0

To solve this quadratic equation, you can factor it:

(L - 7)(L + 4) = 0

Now, set each factor equal to zero and solve for L:

L - 7 = 0

L = 7

L + 4 = 0

L = -4

Since the length of a rectangle cannot be negative, hence the length of the rectangle is 7 units.

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Answer:

1.04719755 or π/3

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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yes, he is right all distance is the same from the origin point to any side of the circle same as radius which is half a line starts at any side of the circle and ends at the origin point.

Mason is correct.

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

A circle centered at the origin with a radius of 4 units can be represented by the equation:

x² + y² = r²

Substituting the coordinates of the point (4, 4), we have:

4² + 4² = r²

16 + 16 = r²

32 = r²

Taking the square root of both sides, we get:

r = 4√2

Therefore,

The circle centered at the origin with a radius of 4 units has an equation of x^2 + y^2 = 32.

Point (4, 4) satisfies this equation since:

4² + 4² = 32

16 + 16 = 32

32 = 32

Thus,

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .

A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.

The following characteristics define a basic parabola:

Thus, from the given graph the value are obtained as:

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H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.

A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.

Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.

Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .

S = “On input (M, B)

This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.

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The regular selling price of the jewelry is $253.00. The sale price for the jewelry is $189.75. And the rate of markdown is 25%.

A jewellery store paid a unit price of $250 less 40%, 16 1/3 %, for a shipment of designer watches . The store's overhead is 65% of cost and the normal profit is 55% of cost.

Overhead and Profit means those costs incurred by you and paid to a General Contractor to perform and oversee covered repairs to the insured location. “Overhead and Profit” does not apply to independent or specialty contractors including, but not limited to, roofers, plumbers, electricians and painters.

It is given that the unit price of the watch is $250 and the discount rates are 40%, 16 +2/3 or 16.666666667%, and 8%. Therefore the purchase price of watches per unit can be estimated as:

Purchase price of watches per unit = Unit price*(1- first discount %)(1-second discount %)(1-third discount %)

Purchase price of watches per unit = 250*(1-40%)(1-16.66666667%)(1-8%)

Purchase price of watches per unit =115

Now, the overhead expense is 65% of the cost. So the overhead amount is Overhead amount = 65% of the cost

Overhead amount = 115*65%

Overhead amount = 74.75

Now, the profit is 55% of the cost. So

Profit amount = Cost *profit %

Profit amount =115*55%

Profit amount =63.25

a. Thus, the regular selling price can be estimated as:

Regular selling price = Unit purchase cost + overhead + profit

Regular selling price =115+74.75+63.25

Regular selling price =253.00

Therefore, the regular selling price of the watches would be $253.00

b. The sale price to break even would be equal to the cost of the watch plus overhead. It is the amount that is required to cover only the total cost of the product. So,

Break-even price = Cost + overhead

Break-even price =115 + 74.75

Break-even price = 189.75

Therefore, the break-even price is $189.75.

c. From above, the regular selling price is 253.00 and the break-even price is 189.75. Thus,

Mark-down rate to sell at break-even price = (Regular selling price-Breakeven price)/Regular selling price.

Mark-down rate to sell at break-even price = (253-189.75)/253

Mark-down rate to sell at break-even price = 0.25 or 25%

Therefore, the mark-down rate is 25%.

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Answer:

45/28

Step-by-step explanation:

6/7+3/4

The least common multiple of 7 and 4 is 28.

Convert 6/7 and 3/4 to fractions with the denominator of 28

24/28+21/28

Since the denominators are now the same, add the numorators to get 45/28

Answer:3 units up four units to the left

Step-by-step explanation:

4/9 of the students are boys thus 5/9 students are girls.

Let " x " be the number of all students.

So we have :

5/9 × x = 90

Multiply both sides by 9/5

5/9 × 9/5 × x = 90 × 9/5

1 × x = 9 × 9 × 10 × 1/5

x = 81 × 2

x = 162

_______________________________

number of boys = 4/9 × x

n o boys = 4/9 × 162

n o boys = 162/9 × 4

n o boys = 18 × 4

n o boys = 72

Answer:

3000+500+60+8

Step-by-step explanation: