If y varies directly with x and y is 18 when x is 6, which of the following represents this situation?

The  exponential function that goes through the point (2, 19) is:

f(x) = sqrt(19)^x
f(x) = 4.36^x (rounded to two decimal places)

We are given a point that lies on the graph of the exponential function f(x) = a^x. The point is (2, 19), which means that when x = 2, f(x) = 19.

Plugging these values into the function, we get:

19 = a^2

To solve for a, we take the square root  of both sides:

sqrt(19) = sqrt(a^2)
sqrt(19) = a

Therefore, the exponential function that goes through the point (2, 19) is:

f(x) = sqrt(19)^x
f(x) = 4.36^x (rounded to two decimal places)

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Answer:

y² = 36x

Step-by-step explanation:

Parabola opens right.

Thus equation is from; y² = 4ax

And focus is at (a, 0)

Since we are given focus at (9, 0),it implies that a = 9

Thus, equation of parabola is;

y² = 4 × 9 × x

y² = 36x

Answer:

a) If Thaddeus is not wrong, his monthly income is $6,185.

x/12.37 = 100/0.2

0.2x = 1237

x = 1237/0.2x

x = 6,185

b) If Thaddeus's friend is correct, Thaddeus's monthly income is $618.5

x/12.37 = 100/2

2x = 1237

x = 1237/2x

x = 618.5

If Thaddeus is not wrong, his monthly income is $6,185.

If Thaddeus's friend is correct, Thaddeus's monthly income is $618.5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Thaddeus shakes his head as he pays $12.37 to the clerk for lunch.

a) If Thaddeus is not wrong then let his income be x.

So, x/12.37 = 100/0.2

0.2x = 1237

x = 1237/0.2x

x = 6,185

b) If Thaddeus's friend is correct

x/12.37 = 100/2

2x = 1237

x = 1237/2x

x = 618.5

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The exponential function y = \(3^x\) grows at a faster rate than the quadratic function for x > 0.

The exponential function that grows at a faster rate than the quadratic function for x > 0 is y = \(3^x\).

To see why, let's first look at the rate of change of the quadratic function.

We can find this by looking at the differences between consecutive y-values:
1 - 0 &= 1
3 - 1 &= 2
12 - 3 &= 9
27 - 12 &= 15
$$We can see that the rate of change is increasing as x increases.

For example, the rate of change between the first two points is 1, while the rate of change between the last two points is 15.

However, this rate of change is still constant within each interval of x-values.

y = \(3^x \\\)  

Let's take a look at its y-values for the same x-values as in the table:
\(3^0\) &= 1

\(3^1\) &= 3
\(3^2\) &= 9
\(3^3\) &= 27
$$We can see that the rate of change is not constant, but rather increasing, just like in the quadratic function.

However, the rate of change is greater for y = \(3^x\).

For example, the rate of change between the first two points is 2, while the rate of change between the last two points is 18.

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Answer:

330

or -30

Step-by-step explanation:

Answer:

m<a = 44°

Step-by-step explanation:

Left triangle:

95 + 39 + x = 180

x = 46

Right triangle:

46 + 90 + a = 180

a = 44

Answer:

ABS Error: 0.05 cm

PERC Error: 0.40%

Step-by-step explanation:

Absolute error: Absolute difference between the actual dimension, and its measure. Measured in the same dimension as what we're measuring

(Remember the absolute)

ABS Err: | 12.25 cm - 12.2 cm | = 0.05cm

Percent error: Percentual difference between the actual dimension and its measure. Always measured in Percents

PERC Err: | (12.25 - 12.20) | / 12.25 = 0.0040 ≈ 0.40%

a) E(Y) is equal to 200. b) The pdf of Y is given by f_Y(y) = (1/5)y(1/2)e(-y/10), which is determined using the transformation method.

Let X have an exponential distribution with mean 10 and Y = X^2.

a. E(Y) = E(X^2) = Var(X) + [E(X)]^2 = 2\([10]^2\) = 200.

b. To find the pdf of Y, we use the transformation method.

Let g(x) = x^2 and h(y) = y^(1/2).

Then, g’(x) = 2x and h’(y) = (1/2)y^(-1/2).

Using the formula for the pdf of a transformed random variable, we get:

f_Y(y) = f_X(h^(-1)(y)) * |h’(y)|

where f_X(x) is the pdf of X.

Since X has an exponential distribution with mean 10, its pdf is given by:

f_X(x) = (1/10)\(e^(-x/10)\)

Using h(y) = y^(1/2), we get: \(h^(-1)(y) = y^2\)

Using g’(x) = 2x and\(h’(y) = (1/2)y^(-1/2)\), we get:

|g’(\(h^(-1)\)(y))h’(y)| = |\(2y^(1/2)\)|

Therefore, the pdf of Y is given by:

f_Y(y) = f_X(\(h^(-1)\)(y)) * |h’(y)|

= (1/10)e(-(\(y(1/2))^2/10) * |2y^(1/2)\)|

= (1/5)y(1/2)e(-y/10)

We use the formulas for the mean and variance of an exponential distribution to find E(Y). To find the pdf of Y, we use the transformation method. We first find the inverse function h^(-1)(y), then calculate |g’(h^(-1)(y))h’(y)|, and finally use the formula for the pdf of a transformed random variable.

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Answer:

\(1~3/4\)

Step-by-step explanation:

Let \(k\) be the amount of pork Mike uses. Then, he uses \(3k\) beef.

We know he uses 7 pounds, of meat so we want to solve \(3k+k=7\).

Combining like terms on the left side gives \(4k=7\).

We can divide both sides by \(4\) to get \(k=7/4=1~3/4\).

So, the answer is \(\boxed{1~3/4}\).

Solution:

Given:

Rereading the phrase carefully:

Equation created: 7d = 105

Answer: To subtract mixed fractions with different denominators, you need to convert the mixed fractions to equivalent fractions with a common denominator. Once the fractions have a common denominator, you can simply subtract the numerators and keep the denominator the same.

Example:

the difference of 2 1/3 and 1 3/4 is 5/12.

Step-by-step explanation:

First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3

Next, convert 1 3/4 to an improper fraction: 1 3/4 = 7/4

Now, both fractions have the same denominator, 3. So, you can subtract the numerators:

7/3 - 7/4 = (7 * 4 - 7 * 3) / (3 * 4) = 28/12 - 21/12 = 7/12

Finally, convert the answer back to a mixed fraction: 7/12 = 7 ÷ 12 =  5/12.

Answer: N = 54

Step-by-step explanation:

Not 100% sure

Answer:

11

Step-by-step explanation:

x + 4 = 15

x = 15 - 4 {transportation}

× = 11

So the answer is 11

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced, resulting in a more accurate assessment of the effect of the independent variable on the dependent variable.

To minimize the variation between individuals, their scores are evaluated within the same group rather than comparing them across different groups.

The within-groups ANOVA method utilizes identical individuals in different conditions or treatments to counteract personal variances, thereby enabling a more accurate measurement of the independent variable's impact.

By adopting this method, the analysis gains greater statistical strength, resulting in a more heightened aptitude to identify genuine effects of the independent factor on the dependent element.

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The dot product of vectors a and b  || a |= 6,|| b ||= 4 and the angle between the vectors θ = π/3 is (c) 12.

The dot product of two vectors, we can use the formula:

a · b = ||a|| ||b|| cos(theta)

where ||a|| and ||b|| represent the magnitudes of vectors a and b, respectively, and theta is the angle between the vectors.

In this case, we are given that ||a|| = 6, ||b|| = 4, and the angle between the vectors is theta = π/3.

Substituting these values into the formula, we have:

a · b = 6 × 4 × cos(π/3)

To evaluate cos(π/3), we can use the fact that it is equal to 1/2. So we have:

a · b = 6 × 4 × 1/2

= 12

Therefore, the dot product of vectors a and b is 12.

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Answer:

Torture

Step-by-step explanation:

Instant pain

If the long-term demand for oranges is the same as the short-term demand, a binding price ceiling will result in a shortage that is larger in long-run demand than the short-run demand. So the answers are shortage and larger.

A shortage occurs when there is a difference between the quantity that is supplied and the quantity that is required of a product, service, or resource. Surplus is a term used to describe situations where there is more supply than demand for a product, service, or resource.

So when the long-run demand is the same as the short-run demand, binding price ceilings typically result in a shortage when there is a lack of supply of products. And, the result will be larger in the case of the long run compared to the short run. Therefore, the first blank can be filled with shortage and the second blank with larger.

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There are 11,232,000 license plates consisting of three letters followed by three digits with no letter or digit repeated.

We can solve this problem using permutation, as we need to find the number of arrangements of three letters followed by three digits with no repetition.

There are 26 letters in the alphabet, so we can choose the first letter in 26 ways. For the second letter, we can choose from the remaining 25 letters, as we cannot use the same letter twice. Similarly, we can choose the third letter in 24 ways.

For the first digit, we have 10 options (0 to 9). For the second digit, we can choose from the remaining 9 digits (we cannot use the same digit twice). Similarly, we can choose the third digit in 8 ways.

Using the multiplication principle, we can find the total number of possible license plates:

26 × 25 × 24 × 10 × 9 × 8 = 11,232,000

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Answer:

x = 50

Step-by-step explanation:

You are correct.

x + m<PQS + m<PSQ = 180

m<PQS = m<QRT = 70

m<QST + m<PSQ = 180

120 + m<PSQ = 180

m<PSQ = 60

x + 70 + 60 = 180

x + 130 = 180

x = 50

Great job!

The volume of the oblique rectangular prism is 216 m³.

How to calculate the volume of an oblique rectangular prism?

The volume of an oblique rectangular prism is given by the formula:

V = l * w * h

Where l  and w are the length and width of the base respectively, and h is the perpendicular distance between the bases

In this case, l = 7.5 m and w = 4.5 m

Using trig. ratio:

tan 65 = h/3

h = 3 * tan 65

h = 6.4 m

Thus,

V = 7.5 * 4.5 * 6.4

V = 216 m³

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Answer:

x=30

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\sqrt{(x + 2)(x - 3)} = 0 \\\\ (x + 2)(x - 3) = 0 \\\\\ x^2 - 3x + 2x - 6 = 0 \\\\ x^2 - x - 6 = 0 \\\\ \Delta = (- 1)^2 - 4.1.(- 6) \\\\ \Delta = 1 + 24 \\\\ \Delta = 25 \\\\ x_1 = \frac{1 + \sqrt{25}}{2} = \frac{ 1 + 5}{2} \\\\\ x_1 = 3 \\\\\\ x_2 = \frac{1 - \sqrt{25}}{2} \\\\\\ x_2 = \frac{1 - 5}{2} \\\\\ x_2 = - 2\)

S = {x E R/x = 3 and x = - 2}

I hope I've helped you

Answer:

It's all integers x such that -1<=x<=2.

Step-by-step explanation:

The domain is the x values for which the relation exists.

Lets read from left to right.

First point I see from left exists at x=-1, next one at x=0, then x=1, and finally at x=2.

So it's all integers x such that -1<=x<=2.

*<= means less than or equal to

Answer:

\(26.666666667\)

Step-by-step explanation:

To find the volume of a pyramid, you can use the formula:

Volume = (1/3) * base area * height

If the base is a rectangle, the base area is calculated by multiplying the length by the width.

Let's call the original length "L", the original width "W", and the original height "H".

The volume of the original pyramid is:

(1/3) * L * W * H = 40 cubic inches

If the length of the base is doubled, the new length is 2L.

The width is tripled, so the new width is 3W.

The height is increased by 50%, so the new height is 1.5H.

The volume of the new pyramid is:

(1/3) * (2L) * (3W) * (1.5H) = (2/3) * L * W * H = (2/3) * 40 cubic inches = 26.666666667 cubic inches.

So the volume of the new pyramid is approximately 26.666666667 cubic inches.

Answer:

B.) An isosceles triangle has at least two sides with equal measures.

Step-by-step explanation:

There are two equal sides and two equal angles in an isosceles triangle. There should be at least 2 equal sides for an Isosceles triangle. This means, even an equilateral triangle is an Isosceles triangle. In this case, at least two equal sides are 8 inches each. This is why the correct answer is 'Yes; an isosceles triangle has at least two sides that have equal measures.'

Wxndy~~

The interest charges of Culver Inc. is $42.86. Therefore, this calculation can be used to find the interest charges of a company that has earnings before interest and taxes (EBIT) and before-tax times-interest-earned ratio.

Culver Inc. is a company that has earnings after interest but before taxes of $300. The before-tax times-interest-earned ratio of the company is 7.00. We need to calculate the interest charges of the company. The interest charges can be calculated by using the formula;Interest Charges = Earnings before Interest and Taxes (EBIT) / Times Interest EarnedRatio (TIE)Since the company has a TIE ratio of 7.00, this means that the company earns seven dollars in operating income for each dollar of interest paid. Therefore, we can use the following formula to find the interest charges;Interest Charges = $300 / 7.00Interest Charges = $42.86

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Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

\(a_n=a_1+\left(n-1\right)d\)

\(18-13=5,\:\quad \:23-18=5\)

As the difference between all the adjacent terms is the same.

so

\(d=5\)

\(a_1=13\)

Arithmetic sequence sum formula

\(n\left(a_1+\frac{d\left(n-1\right)}{2}\right)\)

Put the values

\(d=5\)

\(a_1=13\)

\(n=47\)

\(=47\left(13+\frac{5\left(47-1\right)}{2}\right)\)

\(=47\left(13+\frac{5\left(47-1\right)}{2}\right)\)

\(=47\left(13+115\right)\)

\(=47\cdot \:128\)

\(=6016\)

Thus, the sum of the first 47 terms of the given series = 6016

Answer:

2/3 pound of dough is left

Step-by-step explanation:

Amount of dough available = 6 pounds

The amount used in making sandwich rolls = 8/9 of the total amount

= \(\frac{8}{9} \times6 = 5\frac{1}{3} pounds\)

Therefore, amount of dough left over \(= 6- 5\frac{1}{3} = \frac{2}{3} \\\)

Hence, 2/3 pounds of dough is left

Answer:

C. : 5t

--

Once we find out the number of tables at the reception, we can then multiply the number of tables to 5t.