Harry took a loan from the bank.
DDD represents Harry's remaining debt (in dollars) after ttt months.
D=-200t+9000D=−200t+9000D, equals, minus, 200, t, plus, 9000
What was the size of Harry's loan?

Mary added [tex]$24 \frac{1}{2}[/tex] cups of sugar.

The ratio of flour to sugar exists at 9 cups: 2 4/7 cups

Utilizing equivalent ratios, given that 7 cups of sugar was utilized,

Let cups of flour needed = x such that our equation becomes

flour/sugar[tex]$ =\frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]  

[tex]$ \frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]

Convert mixed numbers into improper fractions

[tex]$2 \frac{4}{7}= \frac{18}{7}[/tex]

simplifying the above equation, we get

[tex]$\frac{9}{\frac{18}{7} } = \frac{x}{7}[/tex]

= [tex]$24 \frac{1}{2}[/tex]

x = 24.5

The value of x = 24.5.

Therefore, [tex]$24 \frac{1}{2}[/tex] cups of sugar exist required.

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Answer:

The answer is 3

Step-by-step explanation:

List all prime factors

15:1,3,5,

27:1,3,

Biggest one is 3

Answer:

the answer is 3

Step-by-step explanation:

cuz the prime factors of 27 is 1,3,and 27

while 15 is 1, 3 ,5 and 15

I hope this helps

Answer: 2

Step-by-step explanation:

When a^b = c, loga(c) = b

So b^5 = 32 and b is 2

Answer:

I don't know what are you saying bro

The original price of the item is $180

The values given in the question are;

Actual cost of the item Joyce bought= $108
The item was sold 40 percent off the original price

The original price can be calculated as follows

The first step is to subtract 40% from 100%

100%- 40%

= 60%

Let x represent the original price of the item

60/100x= 108

0.6x= 108

Divide both sides by the coefficient of x which is 0.6

0.6x/0.6= 108/0.6

x= 180

Thus, the original price of the item is $180

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Answer:

[tex]a_{n} = -3n + 10[/tex]

Step-by-step explanation:

The arithmentic function formula is:

[tex]a_{n} = a_{1} + d(n-1)[/tex]

Let's plug in what we know. [tex]a_{1}[/tex] (the first term in our sequence) is 7. d (the common difference) is -3. This means we are subtracting 3 every time.

Plugging that in to the formula, we get

[tex]a_{n} = 7 -3(n-1)[/tex]

Now we distribute and combine like terms.

[tex]a_{n} = 7 - 3n +3[/tex]

[tex]a_{n} = 10 - 3n[/tex]

Change the order to fit the format and you get

[tex]a_{n} = -3n + 10[/tex]

[tex]30 \: percent \: alcohol \: in \: 260 \: ml \\ alcohol = 0.3 \times 26 0= 78 \: ml[/tex]

[tex]c( \gamma ) = \frac{78 + 0.95\gamma }{260 + \gamma } \times 100[/tex]

[tex]c( \gamma ) = 75[/tex]

[tex] \frac{78 + 0.95\gamma }{260 + \gamma } = 0.75[/tex]

[tex]78 + 0.95\gamma = 0.75 \gamma + 195 \\ 0.2 \gamma = 117 \\ \gamma = 585[/tex]

[tex]we \: need \: 585 \: ml \: of \: 95% \: alcohol[/tex]

Answer:

You will need 585 mL of the 95% solution.

Step-by-step explanation:

It's easy to show that [tex]7\tan(4x)[/tex] is strictly increasing on [tex]x\in\left[0,\frac\pi8\right][/tex]. This means

[tex]M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3[/tex]

and

[tex]m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7[/tex]

Then the integral is bounded by

[tex]\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)[/tex]

[tex]\implies \displaystyle \boxed{\frac{7\pi}{48}} \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le \boxed{\frac{7\sqrt3\,\pi}{48}}[/tex]

Answer:

=> 42 ..

Step-by-step explanation:

Given : a = 6

=> a × 7

=> 6 × 7

=> 42

The missing length of the box with square base is 20.370 inches.

This box can be represented by a right prism, whose volume (V), in cubic inches, is the product of the area of the base (A), in square inches, and the height of the box (h), in inches. The area of the base is equal to the square of the side length (l):

V = l² · h      (1)

If we know that V = 2 200 in³ and l = 108 in, then the height of the box is:

h = V / l²

h = (2 200 in³) / (108 in)

h = 20.370 in

The missing length of the box with square base is 20.370 inches.

The statement presents typing mistakes, correct form is shown below:

A box with a square base has a side length of 108 in. What is the length of the box if its volume is 2 200 in³?

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Answer:

30°

Step-by-step explanation:

[tex]\frac{195-(8x+17)}{2}=5x-10 \\ \\ 178-8x=10x-20 \\ \\ 198=18x \\ \\ x=11[/tex]

So, this means arc FH measures 105 degrees.

Since the circumference of a circle measures 360 degrees, arc EF measures 60 degrees.

By the inscribed angle theorem, angle EHF measures 30°.

Answer:

6.32

Step-by-step explanation:

The formula we use to find the distance between two points is:

[tex]\sqrt{(x_1-x_2)+(y_1-y_2)}[/tex]

The x1 is -3, the x2 is 5, the y1 is -4, and lastly, the y2 is 1.

If we input these numbers in the equation, we end up with:

[tex]\sqrt{(-3-5)+(-4-1)}[/tex]

= [tex]\sqrt{(-8) (-5)}[/tex]

= [tex]\sqrt{40}[/tex]

= [tex]2\sqrt{10}[/tex]

= 6.32455532

Rounded to the nearest hundredth is 6.32

Using it's concept, the integer numbers in the data-set are given as follows:

6/1, -14, 56/7.

The other numbers, -74.48 and 3/17, are not integers.

Integer numbers are numbers that have no decimal part. They can be represented by pure numbers, either negative or positive, or also fractions that result in an exact division.

In this problem, we have that:

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The pounds of alloy that contains 26% copper that would be used is  23.42 pounds.

The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.

0.26a + 0.69b = (53 x 0.5)

0.26a + 0.69b = 26.50 equation 1

a + b = 53 equation 2

Where:

Multiply equation 2 by 0.26

0.26a + 0.26b = 13.78 equation 3

Subtract equation 3 from equation 2

12.72 = 0.43b

b = 12.72 / 0.43

b = 29.58 pounds

a = 53 - 29.58 = 23.42 pounds

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The x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is (17, 11)

The midpoint of a line is the point that bisects or divides the line into two equal parts

If the line JK is partitioned into the ratio 1:4 with the following coordinates

J(-15, -5) and K(25, 15)

Using the expression below;

M(x, y) =[mx1+nx2/m+n, my1+ny2/m+n]

Substitute the ratio and the coordinates

M(x, y) =[1(-15)+4(25)/4+1, 1(-5)+4(15)/1+4]

M(x, y) = [(85)/5, 55/5]

M(x, y) = (17, 11)

Hence the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is ((17, 11)

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Answer:   so there would be 1

23                                                

3   21

2   20

Step-by-step explanation:

Answer: 24,000

Step-by-step explanation:

Based on the data recorded by Isabella, it can be concluded the cube is rather fair.

Based on the data, here are the results:

This implies, in total Isabella got the same number between five and seven times. For example, the number 2 was obtained 5 times, but the number 3 was obtained 7 times.

Even though Isabella did not get the same number of times each number, the dice is rather fair because by rolling the dice thirty six times you will obtain the same number at least five times.

Moreover, there is not a big difference in the number of times you obtain each number.

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The interpretation based on the confidence interval given is that the population mean will fall within the interval.

Number of observations = 10

Sample mean = 2.60

Standard deviation = 1.07

The degree of freedom will be:

= n - 1

= 10 - 1 = 9

Confidence level = 95% = 0.95

Level of significance = 1 - 0.95 = 0.05

The value of the t critical from the t table will be 2.262.

The margin of error will be:

= 2.262 × 1.07/✓10

= 0.765

We get the 95% confidence interval for the population mean. This will be:

(2.60 - 0.765( <= U =(2.60 + 0.765)

1.83 <= 3.37

Therefore, the interpretation is that the population mean will fall within the interval.

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The mean, median, and mode are;

median=77

Mean=73.33

Mode= 78, 67

This is further explained below.

Generally, The middle number in a list that is arranged from smallest to greatest is referred to as the median. On the list, the value that occurs most often is known as the mode. Therefore

median=77

Generally, In mathematics, particularly statistics, the term "mean" may refer to a number of different concepts. The purpose of each mean is to summarize a certain collection of data, often for the purpose of gaining a better understanding of the overall value of a specific data set.

A dataset's mean (also known as the arithmetic mean, which is distinct from the geometric mean) is calculated by dividing the sum of all of the values in the dataset by the total number of values in the dataset. It is the measure of central tendency that is used the most often, and it is sometimes referred to as the "average."

[tex]mean=\frac{\sum x}{n}\\\\Mean=\frac{78+67+98+50+67+78+67+77+78}{9}[/tex]

Mean=73.33

Mean=73.3 in one dp

In conclusion, The mode is the number that appears the most often, or the number that stands out as having the most occurrences overall. The number 2 is the mode of the sequence 4, 2, 4, 3, 2, 2 because it appears three times, which is more than any other number in the sequence.

The mode of 78, 67, 98, 50, 67, 78, 67, 77, 78  is

Mode= 78, 67

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The value of the expression (a - b)² from the given equations is; 16

We are given the two equations as;

a + b = 10   -----(eq 1)

ab = 21    ------(eq 2)

From eq 1, square both sides;

(a + b)² = 10²

a² + 2ab + b² = 100

a² + b² = 100 - 2ab

We are given ab = 21. Thus;

a² + b² = 100 - 2(21)

a² + b² = 58

Now, we know that (a - b)² = a² - 2ab + b²

Thus;

(a - b)² = 58 - 2(21)

(a - b)² = 16

Complete question is;

If a + b = 10 and ab = 21, then the value of (a - b)² is?

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Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is:

2/39.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Hence the probability will be given as follows:

p = 4/13 x 2/12 = 4/13 x 1/6 = 2/13 x 1/3 = 2/39.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$132.90\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years \end{cases} \\\\\\ 132.90 = (6000)(0.055)(t)\implies \cfrac{132.90}{(6000)(0.055)}=t\implies \cfrac{443}{1100}=t \\\\\\ \stackrel{\textit{converting that to days}}{\cfrac{443}{1100}\cdot 365} ~~ \approx ~~ 147~days[/tex]

now, if we move back from August 14th by 147 days backwards, that'd put us on March 20th.

[tex]x ^{3} + 5x {}^{2} - 8 r - 20 = 0 \\ x { }^{3} + 5x {}^{2} - 8r - 20(x {}^{3} + 5x {}^{2} ) = 0 - (x {}^{3} + 5x {}^{2} ) \\ - 8r - 20 = - (x {}^{3} + 5x {}^{2} ) \\ \\ - 8r - 20 + 20 = - (x {}^{3 } + 5x {}^{2} ) + 20 \\ \\ - 8r = x {}^{3} - 5x {}^{2} + 20 \\ \\ [/tex]

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The amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars

The data from the questions says that the cost of the house = $245000

The down payment amount amount is 45000

Given that they already paid 45000 from the cost of the house, the mortgage would be 245000 - 45000

= $200000

The cost of 1.5 points is the same as the cost of 1.5% of the mortgage of this house.

This is calculated as 0.015 x 200000

= $3000

The conclusion is that the amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars

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Under the straight-line depreciation method, the depreciation expenses for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, for Perdue Company, are as follows:

Year Amount

Year 1 $2,858.33 ($11,4333.33 x 3/12)

Year 2 $11,433.33

Year 3 $11,433.33

Year 4 $8,575.01 ($11,433.34 - $2,858.33)

The straight-line method is one of the depreciation methods in use by companies to allocate the cost of plants and equipment over their useful lives.

Under the straight-line method, the depreciable amount (cost less residual value) is divided by the estimated useful life.

Other depreciation methods include the unit-of-production, double-declining-balance, and the sum-of-the-years-digit methods.

Equipment cost = $36,100

Residual value = $1,800

Depreciable amount = $34,300 ($36,100 - $1,800)

Estimated useful life = 3 years

Annual depreciation = $11,433.33 ($34,300/3)

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Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by the straight-line method.

The graph of the function, f(x) = (1/4)ˣ, can be seen in the attached graph, following the given steps.

In the question, we are given the function, f(x) = (1/4)ˣ.

Step 1, has asked us to find the initial value of the graph, f(0).

This can be calculated by substituting x = 0, in the given function, which gives us:

f(0) = (1/4)⁰ = 1.

Step 2, has asked us to plot the initial value of the function at (0, 1). This is plotted using the graphing tools.

Step 3, has asked us to evaluate f(1) and f(-1). By substituting x = 1, and x = -1, we get:

f(-1) = (1/4)⁻¹ = 4,

f(1) = (1/4)¹ = 1/4.

Step 4, has asked us to plot the points (1, 1/4), and (-1, 4). This is plotted using the graphing tools.

Step 5, has made us identify the asymptote y = 0.

Step 6, gives us the final curve for the function, f(x) = (1/4)ˣ.

The provided question is incomplete. The complete question is:

"Graph: f(x) = (1/4)ˣ

Step 1: Calculate the initial value of the function. f(0) =

Step 2: Plot the initial value of the function at (0, 1).

Step 3: Evaluate the function at two more points. f(1) = 1/4, f(-1) = 4

Step 4: Plot the points (1, 1/4) and (-1, 4)

Step 5: Identify the horizontal asymptote of the function. The asymptote is the line y = 0

Step 6: The smooth curve that includes these points and approaches to the asymptote shows the graph of the function"

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