Solve for x: x/3= 7

x= 21
x= 12
x= 7/3
x= 11
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The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less

is 5p + 9h ≤ 45.  

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.

Also, we can only buy two types of books for $45 or less.

Therefore, The inequality representing the context is,

5p + 9h ≤ 45.  (As the cost van be $45 or less not only less)

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Using geometric sequence, a) The fine on day n is $2^n (2 to the power of n). b) It would take log_2(D/2) + 1 days for the fine to reach D dollars.

In this court case, the fine on each subsequent day is equal to the square of the previous day's fine. This means that the fine follows a geometric sequence, where the common ratio is the square of the previous term.

a) To find the fine on day n, we can use the formula for the nth term of a geometric sequence:

a_n = a_1 * r^(n-1)

Where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

In this case, a_1 = 2 (the fine on the first day), r = 2 (the common ratio), and n is the day number. Plugging these values into the formula, we get:

a_n = 2 * 2^(n-1)

So the fine on day n would be 2 * 2^(n-1) dollars.

b) To find how many days it would take the fine to reach D dollars, we can use the formula for the nth term of a geometric sequence and solve for n:

D = 2 * 2^(n-1)

Dividing both sides by 2, we get:

D/2 = 2^(n-1)

Taking the logarithm of both sides with base 2, we get:

log_2(D/2) = n - 1

Adding 1 to both sides, we get:

n = log_2(D/2) + 1

So it would take log_2(D/2) + 1 days for the fine to reach D dollars.

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Answer:

2 and 4

Step-by-step explanation:

Answer:

2 and 4

Step-by-step explanation:

Answer:

(5,354 + x)

or

536.4*x

Step-by-step explanation:

We know that x = 10.

Now we want to write an expression (in terms of x) for the number 5,364.

This could be really trivial, remember that x = 10.

Then:  (x - 10) = 0

And if we add zero to a number, the result is the same number, then if we add this to 5,364 the number does not change.

5,364 = 5,364 + (x - 10) = 5,364 + x - 10

5,364 = 5,354 + x

So (5,354 + x) is a expression for the number 5,364 in terms of x.

Of course, this is a really simple example, we could do a more complex case if we know that:

x/10 = 1

And the product between any real number and 1 is the same number.

Then:

(5,364)*(x/10) = 5,364

(5,364/10)*x = 5,364

536.4*x = 5,364

So we just found another expression for the number 5,364 in terms of x.

The formula for the general term an of the sequence is an = 2n + 3.

Given that the pattern of the first few terms continues.

To find a1, we can substitute n=1 in the formula and use the first term of the sequence, which is 5:

a1 = 5

Therefore, the general term of the sequence is:

an = 5 + 7(n-1) = 7n - 2

The given sequence has a common difference of 7 that is each term in the sequence is obtained by adding 7 to the previous term.

Therefore, the formula for the general term an can be obtained as:

an = a1 + (n - 1)d

where a1 is the first term of the sequence and d is the common difference.

Here, a1 = 5 and d = 7. Substituting these values in the formula, we get:

an = 5 + (n - 1)7

Simplifying this expression, we get:

an = 2n + 3

Therefore, the formula for the general term an of the sequence is          an = 2n + 3

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Answer:

4w + 10

Step-by-step explanation:

If you have any questions feel free to ask

answer: 4w+10

explanation:: distribute;

= (4)(w)+(4)(3)+−2

= 4w+12+−2

combine like terms;

= 4w+12+−2

= (4w)+(12+−2)

= 4w+10

Answer:

Step-by-step explanation:

Answer:

\(\theta \approx 61.93\textdegree\)

Step-by-step explanation:

We can solve for the measure of angle θ in this right triangle using the trigonometric ratio sine, which uses the opposite and hypotenuse sides.

\(\sin(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}}\)

↓ plugging in the given values

\(\sin(\theta) = \dfrac{15}{17}\)

↓ taking the inverse tangent of both sides

\(\sin^{-1}\left(\dfrac{}{}\sin(\theta)\dfrac{}{}\right) = \sin^{-1}\left(\dfrac{15}{17}\right)\)

↓ canceling the inverse functions on the left side ... \(f^{-1}\left(\dfrac{}{}f(x)\dfrac{}{}\right) = x\)

\(\theta = \sin^{-1}\left(\dfrac{15}{17}\right)\)

↓ evaluating using a calculator

\(\theta \approx 61.93\textdegree\)

The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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Answer: C. Infinitely many solutions

Step-by-step explanation: If the answer is <0, then there is no solution; if it is >1, then there is more than one solution; if = 0, then there are Infinitely many solutions

-14(z-5) = -14z +70 can be write as

-14z + 70 = -14z + 70

-14z = -14z

 z= 0

Because the answer is 0 so there Infinitely many solutions

If you can, please give me a Brainliest; thank you!

Answer:

C. Infinite many solutions.

Step-by-step explanation:

Simplify the left side of the equation. Note the parenthesis. Distribute -14 to all terms within the parenthesis:

-14(z -  5) = -14z + 70

-14z + 70 = -14z + 70

C. Infinitely many solutions is your answer, as no matter what number you plug in for the variable z, the equation would still be true.

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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

The given problem is asking for a test to see if the sample mean is significantly different from 85 at the 0.05 level. To solve the problem, we can use the following formula:$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$where$\bar{x}$ = sample mean$\mu$ = population mean$s$ = sample standard deviation$n

$ = sample sizeTo calculate the t-value, we need to calculate the sample mean and the sample standard deviation. The sample mean is calculated as follows:$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$where $x_i$ is the score of the $i$th student and $n$ is the sample size.

Using the given data, we get:$$\bar

{x} = \frac{78+89+67+85+90+83+81+79}{8}

= 81.125$$The sample standard deviation is calculated as follows:$$

s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}$$Using the given data, we get:$$

s = \sqrt{\frac{(78-81.125)^2+(89-81.125)^2+(67-81.125)^2+(85-81.125)^2+(90-81.125)^2+(83-81.125)^2+(81-81.125)^2+(79-81.125)^2}{8-1}}

= 7.791$$Now we can calculate the t-value as follows:$$

t = \frac{\bar{x} - \mu}{\frac{s}

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Answer:

See Below

Step-by-step explanation:

An inverse relationship between x and y means that while x goes up, y goes down, or vice versa.

This type of relationship can be seen in business or finance.

Answer:

Approximately 2254 people.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

ㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇㅇ

Answer:

A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction

Step-by-step explanation:

Given:

(2x + 5) / (x² - 3x) - (3x + 5) / (x³ - 9x) - (x + 1) / x² - 9

Factor the denominators

(2x + 5) / x(x - 3) - (3x + 5) / x(x - 3)(x + 3) - (x + 1) / (x - 3)(x + 3)

Lowest common multiple of the 3 fractions is x(x - 3)(x + 3)

= (2x+5)(x+3) - (3x + 5) - (x + 1)x / x(x - 3)(x + 3)

= (2x²+6x+5x+15) - (3x + 5) - (x² + x) / x(x - 3)(x + 3)

= 2x² + 11x + 15 - 3x - 5 - x² - x / x(x - 3)(x + 3)

= x² + 7x + 10 / x(x - 3)(x + 3)

Solve the numerator.

Solve the quadratic expression by finding two numbers whose product is 10 and sum is 7

The numbers are 5 and 2

= x² + 5x + 2x + 10 / x(x - 3)(x + 3)

= x(x + 5) + 2(x + 5) / x(x - 3)(x + 3)

= (x + 5)(x + 2) / x(x - 3)(x + 3)

A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction

Recall,

x(x - 3)(x + 3) is a factor of x³ - 8x

A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction

(x + 5)(x + 2) / x³ - 9x

B. StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction

(x + 5)(x + 4) / x³ - 9x

C. StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction

2x + 11 / x³ - 12x - 9

D. StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction

3(x + 2) / x² - 3x

At an angle of 270 degrees (or 3π/2 radians) on a circle with a radius of 2 and center at (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

To find the x and y coordinates at an angle of 270 degrees (or 3π/2 in radian measure) on a circle of radius 2 with center (0, 0), we can use the trigonometric definitions of sine and cosine.

The x-coordinate (x-value) represents the horizontal position on the circle, while the y-coordinate (y-value) represents the vertical position.

For a point on the unit circle (circle with radius 1) at a given angle θ, the x-coordinate is given by cos(θ) and the y-coordinate is given by sin(θ).

In this case, the circle has a radius of 2, so we need to multiply the cosine and sine values by 2 to get the x and y coordinates, respectively.

Using the angle 270 degrees (or 3π/2 in radian measure):

x-coordinate = 2 * cos(3π/2)

y-coordinate = 2 * sin(3π/2)

Evaluating these expressions:

x-coordinate = 2 * cos(3π/2) = 2 * 0 = 0

y-coordinate = 2 * sin(3π/2) = 2 * (-1) = -2

Therefore, at an angle of 270 degrees (or 3π/2 radians) on the circle of radius 2 with center (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

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Answer:

M.P=Rs.6000

Sales tax=10%

S.P including sales tax=6000+

100

10

×600

⇒6000+600=Rs.6600

Discount=15%

∴ S.P after discount=6600−15%of6600

⇒6600−

100

15

×6600

⇒6600−990=Rs.5610

Answer:

y = x + 40

Step-by-step explanation:

I'm assuming to simplify this.

Use the distribution property first.

y = -4x - 8 · 4x + 32

Combine like terms.

y = x · 8 + 32

Solve.

y = x + 40

Hope this this helps!

The domain of ggg is option D: -7 ≤ x ≤ 4.

To determine the domain of a function, we need to identify the set of all possible values for the independent variable, in this case, x, for which the function is defined.

In option D, the domain is specified as -7 ≤ x ≤ 4. This means that x can take any value within the closed interval from -7 to 4, inclusive.

In other words, the domain of ggg includes all real numbers between -7 and 4, including -7 and 4 themselves. This interval represents the range of values for x that satisfy the given conditions for the function ggg.

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After 6 days, the population size was 10 members, calculated using the equation \(Nt = N0 * e^{(r*t})\)

The population of protozoa grows according to a constant relative growth rate of 0.7507 per member per day. On day 0, the population size is 6 members. After 6 days, the population size can be calculated using the equation\(Nt = N0 * e^{(r*t)}\) where Nt is the population size after t days, N0 is the initial population size, and r is the growth rate.

Plugging in the values, we get \(N6 = 6 * e^{(0.7507*6)}\)

Using a calculator, we find that \(N6 = 10.22\), rounded to the nearest whole number 10.

Therefore, the population size of protozoa after 6 days is 10 members.

To summarize, the population of protozoa develops with a constant relative growth rate of 0.7507 per member per day. On day zero, the population size was 6 members. After 6 days, the population size was 10 members, calculated using the equation \(Nt = N0 * e^{(r*t})\)

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Answer:

its purple

Step-by-step explanation:

Answer:

x>dy-c

Step-by-step explanation:

The area of triangle ABC is approximately 2.8 square units. We have two circles, one with a radius of 1 and the other with a radius of 2. The smaller circle is tangent to the larger circle at point D.

The sides AB and AC of triangle ABC are tangent to the circles at points E and F, respectively. We are told that AB and AC are congruent.

First, let's find the length of side AB. Since AB is tangent to the smaller circle at point E, it is perpendicular to the radius DE. Therefore, DE is the height of triangle ABC. DE is also the radius of the smaller circle, which is 1 unit. Hence, DE = 1.

Next, let's find the length of side AC. Since AC is tangent to the larger circle at point F, it is perpendicular to the radius DF. DF is the sum of the radii of the smaller and larger circles, which is 1 + 2 = 3 units. Hence, DF = 3.

Now, we have a right triangle with sides DE = 1 and DF = 3. Using the Pythagorean theorem, we can find the length of side EF:

EF² = DF² - DE²

EF² = 3² - 1²

EF² = 9 - 1

EF² = 8

EF = √8 = 2√2

Finally, we can find the area of triangle ABC using the formula for the area of a triangle:

Area = 1/2 * base * height

Area = 1/2 * AB * EF

Area = 1/2 * 2√2 * 1

Area = √2 square units

Approximating the value of √2 to 1.414, we find that the area of triangle ABC is approximately 2.828 square units or 2.8 square units (rounded to one decimal place).

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The value of the test statistic is1.697.  the degrees of freedom for the t distribution is 67.  the p-value is 0.0967. The p-value is greater than 0.025 but less than 0.975, we do not reject H0 at α = 0.05

(a) The test statistic for a two-sample t-test is given by:

t = (x1 - x2) / sqrt(\(s1^2/n1 + s2^2/n2\))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. Plugging in the given values, we have:

t = (13.6 - 10.1) / sqrt(\(5.8^2/35 + 8.6^2/40\)) ≈ 1.697

b) The degrees of freedom for the t distribution is given by:

df = (\(s1^2\)/n1 + s22/n2)2 / ((s12/n1)2/(n1-1) + (s22/n2)2/(n2-1))

Plugging in the given values, we have:

df = (5.8^2/35 + 8.62/40)2 / ((5.82/35)2/34 + (8.62/40)2/39) ≈ 67

c) The p-value for a two-tailed t-test with 67 degrees of freedom and t = 1.697 is given by: p-value = 2 * P(T > 1.697) ≈ 0.0967

d) At α = 0.05, we reject H0 if the p-value is less than α/2 or greater than 1 - α/2. Since the p-value is greater than 0.025 but less than 0.975, we do not reject H0 at α = 0.05.

Therefore, our conclusion is do not Reject H0. There is insufficient evidence to conclude that 1 − 2 ≠ 0.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

width = 9/2 inches, length = 18 inches

Step-by-step explanation:

Step-by-step explanation:

l = length

w = width

l×w = 81 in²

l = 2w + 9

we can use the identity of the second equation in the first equation :

(2w + 9)×w = 81

2w² + 9w = 81

2w² + 9w - 81 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = w

a = 2

b = 9

c = -81

w = (-9 ± sqrt(9² - 4×2×-81))/(2×2) =

= (-9 ± sqrt(81 + 648))/4 =

= (-9 ± sqrt(729))/4 = (-9 ± 27)/4

w1 = (-9 + 27)/4 = 18/4 = 9/2 in

w2 = (-9 - 27)/4 = -36/4 = -9

a negative solution for a side length does not make any sense, so, width = 9/2 in is the only valid solution.

l = 2w + 9 = 2×9/2 + 9 = 9+9 = 18 in

so, the last answer option is correct.

The fraction of the students that played the trumpet is 1/6

The school band has several students

1/4 play a brass instrument

2/3 of those students play the trumpet

Therefore the fraction of students that paly the trumpet can be calculated as follows

1/4 × 2/3

= 1/6

Hence the fraction of students that play the trumpet is 1/6

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