[tex]What is the logarithmic form of the exponential equation 4^{3} =(5x+4)[/tex]

Answer:

y=9 (3x/9-2) + 18=3x

Step-by-step explanation:

Answer: To find the median credit score, we need to arrange the three scores in order from lowest to highest:

748, 758, 765

The median is the middle value in this ordered list. Since there are three scores, the median is the second score, which is 758.

Therefore, Christine's median credit score is 758.

Step-by-step explanation:

The account has an annual interest rate of 6.80%, compounded continuously.

Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.

The interest rate of the account can be calculated as follows:

Rate = ln(1,698.49/1,051)/(8×ln(1))

Rate = 0.0680 or 6.80%

This means that the account has an annual interest rate of 6.80%, compounded continuously.

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Therefore, the Left Riemann Sum for this function, interval, and number of subintervals is 50.

The top-left corner of these rectangles touched the y=f(x) curve. In other words, the value of f at the subinterval's left endpoint determined the height of the rectangle over that subinterval. This technique is called the left-endpoint estimate because of this.

With left endpoints and n = 5 subintervals, we may use the Left Riemann Sum formula to approximate the area under the curve of f(x) = x2 + 4 over the range [0, 5]:

Left Riemann Sum = ∑[i=1 to n] f(x_i-1) Δx

In this case, a = 0, b = 5, n = 5, and we will use the left endpoints, so:

Δx = (5 - 0)/5 = 1

Using the left endpoints, the subintervals and their left endpoints are:

[0,1],[1,2],[2,3],[3,4],[4,5]

[tex]so,\; x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4.[/tex]

Now we can calculate the Left Riemann Sum:

Left Riemann Sum= [tex]f(x_0)\Delta x + f(x_1)\Deltax + f(x_2)\Deltax + f(x_3)\Deltax + f(x_4)\Deltax[/tex]

= f(0)×1+f(1)×1+f(2)×1+f(3)×1 + f(4)×1

= 4+5+8+13+20

= 50

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Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.

given

a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 3 = 5

b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.

A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.

c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 10 = 1.5

Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

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Answer:

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer: 138

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer:

Option A: The solution is incorrect because the student did not correctly identify the intersection.

Step-by-step explanation:

Solve by elimination method.

5x + 2y = 10; -10x + 2y = 1

Multiply the second equation by -1, then add the equations together.

(5x + 2y = 10)

-1 (-10x + 2y = 1)

Forms:

5x + 2y = 10

10x - 2y = -1

Add these equations to eliminate y.

15x = 9

Then solve 15x = 9 for x:

15x = 9

15/15 = 9/15 (Divide both sides by 15)

x = 3/5

Now that we've found x let's plug it back in to solve for y.

Write down the original equation:

5x + 2y = 10

Substitute 3/5 for x in:

5x + 2y = 10:

5(3/4)+2y=10

2y+3=10

2y+3-3=10+-3

2y=7

2y/2 = 7/2

y = 7/2

x = 3/5 and y = 7/2.

Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.

The integer that represents the change in temperature from morning to afternoon is 18.

The group of counting numbers that can be written without a fractional component includes zero and both positive and negative integers. An integer can, as was already established, be either positive, negative, or zero.

To find the change in temperature from morning to afternoon, we need to subtract the morning temperature from the afternoon temperature:

9.3 F - (-8.7 F) = 9.3 F + 8.7 F = 18 F

Therefore, the integer that represents the change in temperature from morning to afternoon is 18.

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Answer:

Hm

Step-by-step explanation:

The formula to find the circumference of a circle is:

Circumference = 2πr

Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of radius, we get:

Circumference = 2 x π x 6

Circumference = 12π

Circumference ≈ 37.7 cm (rounded to one decimal place)

Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.

Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:

(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth

To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:

(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth

To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):

50/16 = 3.125 gallons of milk

30/16 = 1.875 gallons of broth

Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.

Step-by-step explanation:

Step-by-step explanation:

Perimeter is the total of all three sides added together:

  2x^2 + x        +     3x^2 -3       + ?      =  3x^2 + 2      Simplify a bit on the L

     5x^2  + x  -3     + ?  = 3x^2 + 2           subtract 5x^2 from both sides

                  x-3   + ?    = - 2x^2 + 2           subtract x from both sides

                     -3  + ?   = - 2x^2 - x + 2       finally, add 3 to both sides

                            ?  = - 2x^2 -x + 5

The absolute maximum value of f(x) is 4.5 and it occurs at x = -0.5, and the absolute minimum value of f(x) is -0.241 and it occurs at x = 0.833

To find the absolute maximum and minimum of the function f(x) = 4x^3 - 2x^2 - 5x + 3, we need to take the derivative of the function and set it equal to zero to find the critical points.

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

f'(x) = 12x^2 - 4x - 5

Setting f'(x) = 0, we get:

12x^2 - 4x - 5 = 0

Using the quadratic formula, we get:

x = -0.5 or x = 0.833

Now we need to check the values of f(x) at the critical points and the endpoints of the interval

f(-0.5) = 4(-0.5)^3 - 2(-0.5)^2 - 5(-0.5) + 3 = 4.5

f(0.833) = 4(0.833)^3 - 2(0.833)^2 - 5(0.833) + 3 = -0.241

So the absolute maximum it occurs at x = -0.5, and the absolute minimum occurs at x = 0.833

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Answer:

center : (-3, -1) radius : 4

Answer:

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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Answer: A

Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.

The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.

The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.

The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:

P(vowel and consonant) = P(vowel) x P(consonant)

= 0.25 x 0.75

= 0.1875

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Check the picture below.

so following the template below, a shift 2 units to the left, means C=2

[tex]G(x)=\sqrt{x+2}[/tex]

Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]

Answer:

x = 5

Step-by-step explanation:

given FH is a diameter , then

arc FH = 180°, that is

FG + GH = 180°

103° + GH = 180° ( subtract 103° from both sides )

GH = 77°

the central angle HIG is equal to the arc that subtends it GH , so

∠ HIG = 77°

∠ EIF and ∠ HIG are vertically opposite angles and are congruent , then

∠ EIF = 77°

the arc EF subtends the central angle EIF , so

EF = 77°

the sum of the 3 arcs = 180° , that is

HD + DE + EF = 180

15 + 18x - 2 + 77 = 180

18x + 90 = 180 ( subtract 90 from both sides )

18x = 90 ( divide both sides by 18 )

x = 5

then arc DE = 18x - 2 = 18(5) - 2 = 90 - 2 = 88°

Answer:

We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:

x^2 + 12^2 = 16^2

Simplifying:

x^2 + 144 = 256

x^2 = 112

Taking the square root of both sides:

x ≈ 10.6 feet

Therefore, Brenda is approximately 10.6 feet away from the fish.

The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.

In statistics, the critical value is a value that is used to determine whether to reject the null hypothesis in a hypothesis test. It is based on the chosen level of significance, which is the maximum probability of making a Type I error (rejecting a true null hypothesis). The critical value is determined by the sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.

To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.

Using a t-distribution table with 21 degrees of freedom (n-1), we find that the critical value for a 99% confidence level is approximately 2.819.

Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).

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The mean number of bedrooms in a house in this neighborhood will be: 3.824.

In order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.

Next, we will add the products, and then divide by the total frequency. So we can start as follows:

(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478

Total frequency = 7 + 35 + 56 + 27 = 125

Therefore, the mean number of bedrooms = 478 / 125  approximately 3.824

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Answer:

FV ≈ $5,673.56

Step-by-step explanation:

To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $225 per month)

r is the interest rate per year (in this case, 5%)

n is the number of years (in this case, 2)

Substituting the given values, we get:

FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))

Using a calculator, we get:

FV ≈ $5,673.56

Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.

Answer:

10 feet

Step-by-step explanation:

Let's start by finding the current area of the deck:

Area = length x width = 20 ft x 10 ft = 200 sq ft

If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:

Length = 20 ft + x

Width = 10 ft + x

The new area of the deck will be:

New Area = (20 ft + x) x (10 ft + x)

We know that Ian wants the new area to be triple the original area of 200 sq ft, so:

New Area = 3 x 200 sq ft

New Area = 600 sq ft

Substituting this into the equation above and solving for "x", we get:

(20 ft + x) x (10 ft + x) = 600 sq ft

200 + 30x + x^2 = 600

x^2 + 30x - 400 = 0

(x + 40) (x - 10) = 0

We discard the negative solution, and we get:

x = 10 ft

Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.

To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.

If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.

Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.

Ian should increase both the sides by 10 feet each.

This is a simple mathematics problems related to the topic of mensuration.

Firstly we calculate the current area of the deck:

Area of the deck (rectangle) = l x b

Area of the deck (rectangle) = 20 x 10

Area of the deck (rectangle) =  200 square feet

Since Ian wants to triple the area of the deck, the required area is 600 square feet.

We now look at pairs of numbers multiplying which will give us 600:

(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)

Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.

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well, the markup is 1,776.33 - 1,315,80 = 461.33.

now, if we take 1315.80(origin amount), what is 461.33 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1315.80 & 100\\ 461.33& x \end{array} \implies \cfrac{1315.80}{461.33}~~=~~\cfrac{100}{x} \\\\\\ 1315.8x=46133\implies x=\cfrac{46133}{1315.8}\implies x\approx 35[/tex]

Answer:

Whats the question?

Step-by-step explanation: