Solve the equation. Give the solution in exact form. log 6 [(x + 5)(x - 4)] = 2 . Rewrite the given equation without logarithms. Do not solve for X. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is (Type an exact solution, using radicals as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

The statistic that the value 24.7 represents in this context is the median of the gas mileages for the cars tested.

Popular magazine that tests cars and trucks for mileage on the road and around the city. They report that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% had mileages above 24.7 mpg. The 24.7 mpg statistic represents the median of the gas mileages for the cars tested. This is because the median is the middle value when the data is arranged in ascending order, and in this case, it separates the lower 50% from the upper 50% of the mileages.

The median is the value that separates the data set into two halves. In this case, the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road and the other 50% of the cars tested had mileages above 24.7 mpg. This means that 24.7 mpg is the exact middle value of the distribution of the gas mileages for the cars tested.

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Using the given information we found that the equation of the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

For a parabola with vertex (h, k), the equation is:

y = a*(x - h)^2 + k

Here the vertex is (3, 5), so the equation is:

y = a*(x - 3)^2 + 5

And the y-intercept is y = 1, this means that:

1 = a*(0 - 3)^2 + 5

1 = a*9 + 5

1 - 5 = a*9

-4/9 = a

So the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

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Answer:

I think it is the fourth one

\(y = \frac{1}{8} x + 9\)

Step-by-step explanation:

I hope that is useful for you :)

Answer:

6 toppings

Step-by-step explanation:

The t in this equation represents the amount of toppings.

22 + 0.65t = 26

-22 -22

0.65t = 4

0.65t/0.65 = 4/0.65

t = 6

They could get 6 toppings and the total would be $25.90.

Answer:

6

Step-by-step explanation:

(10+2)/2

6

The values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

The expression p(- x ≤ t22 ≤ x) represents the probability of a t-distribution with 22 degrees of freedom lying between - x and x.

We want to find the values of x such that this probability is 0.98.

We can use a table of t-distribution probabilities or a calculator to find the value of t for which the probability of a t-distribution with 22 degrees of freedom lying between −t and t is 0.98.

This value is , 2.518.

Therefore, we need to solve the inequalities:

-2.518 ≤ -x ≤ 2.518

Solving for x, we get:

-2.518 ≤ -x x ≤ 2.518

Therefore, the values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

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Answer:

x= 104

Step-by-step explanation:

The sum of the angles on a straight line is 180°.

72° +(x +4)°= 180° (adj. ∠s on a str. line)

(x +4)°= 180° -72°

(x +4)°= 108°

x +4= 108

x= 108 -4

x= 104

The confidence limits at a 95% CI for these related samples are (0.14,3.94).

We are given that;

Difference Scores (Friday − Monday) =−1.7 +3.3 +4.3 +6.2 +1.1

Now,

(a) To find the confidence limits at a 95% CI for these related samples, we can use the formula:

\($$\bar{d} \pm t_{\alpha/2,n-1} \frac{s_d}{\sqrt{n}}$$\)

where \($\bar{d}$\) is the mean of the differences, \($s_d$\) is the standard deviation of the differences, $n$ is the sample size and \($t_{\alpha/2,n-1}$\)is the critical value from the t-distribution with \($n-1$\) degrees of freedom

Using the given data, we have:

\($\bar{d} = \frac{-1.7 + 3.3 + 4.3 + 6.2 + 1.1}{5} = 2.04$$s_d = \sqrt{\frac{\sum_{i=1}^{n}(d_i - \bar{d})^2}{n-1}} = \sqrt{\frac{(2.04+1.7)^2 + (3.3-2.04)^2 + (4.3-2.04)^2 + (6.2-2.04)^2 + (1.1-2.04)^2}{4}} = 3.15$$t_{\alpha/2,n-1} = t_{0.025,4} = 2.776$\)

\($$2.04 \pm 2.776 \times \frac{3.15}{\sqrt{5}}$$$$= (0.14, 3.94)$$\)

Therefore, by algebra the answer will be (0.14,3.94).

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Answer:

The answer is C

Step-by-step explanation:

I took the test on edge and got 100%

The statement which must be true according to the box plot is C. The data is skewed and shows that she was equally likely to work more than 3.5 hours or less than 5 hours.

In computing, data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Data is a collection of facts, while information puts those facts into context. While data is raw and unorganized, information is organized. Data points are individual and sometimes unrelated. Information maps out that data to provide a big-picture view of how it all fits together.

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The ATI Capstone Comprehensive Assessment evaluation normally comprises of multiple-choice questions, with 90 to 130 possible answers. Certain versions may also include extra alternative questions kinds, such as fill-in-the-blank or select-all-that-apply

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Answer:

\(\huge\boxed{\sf Discriminant = -4}\)

Step-by-step explanation:

Comparing it with quadratic equation \(ax^2 + bx + c = 0\), we get:

a = 1 . b = 4 and c = 5

So,

Discriminant = \(b^2-4ac\)

D = (4)²-4(1)(5)

D = 16 - 20

D = -4

Hence,

Discriminant = -4

\(\rule[225]{225}{2}\)

Hope this helped!

Answer: The answer is 25! :)

Give brainiest?

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

a. To find the given series i.e.,  5∑n=0(9(2)n)−7(−3)nTo find 5∑n=0(9(2)n)−7(−3)n,

we need to find the first five terms of the series. The given series is,

5∑n=0(9(2)n)−7(−3)n5[(9(2)0)−7(−3)0] + [(9(2)1)−7(−3)1] + [(9(2)2)−7(−3)2] + [(9(2)3)−7(−3)3] + [(9(2)4)−7(−3)4]

After evaluating, we get:

5[(9*1) - 7*1] + [(9*2) - 7*(-3)] + [(9*4) - 7*9] + [(9*8) - 7*(-27)] + [(9*16) - 7*81]15 + 57 + 263 + 1089 + 4131= 5555b.

Given premises: p → q, ¬p → r, r → s.

We are to prove that ¬q → s. i.e.,

Premises: (p → q), (¬p → r), (r → s)

Conclusion: ¬q → s

To prove ¬q → s,

we need to assume ¬q and show that s follows.

Then we use the premises to derive s.

Proof:

1. ¬q        Assumption

2. ¬(¬q)    Double negation

3. p         Modus tollens 2,1 & p → q

4. ¬¬p      Double negation

5. ¬p        Modus ponens 4,3 (Conditional elimination)

6. r         Modus ponens 5,2 (Conditional elimination)

7. s         Modus ponens 6,3 (Conditional elimination)

8. ¬q → s     Conditional introduction (Implication)

Thus, ¬q → s is proven.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent, we need to show that their negation is equivalent. i.e.,

we show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p)Negation of (p ∨ ¬q) = ¬p ∧ q Negation of (q ∧ ¬p) = ¬q ∨ p

Thus, we are to show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p) is equivalent to ¬p ∧ q ↔ ¬q ∨ p

Proof:

¬(q ∧ ¬p)  ≡  ¬q ∨ p       Negation of (q ∧ ¬p)(p ∨ ¬q)   ≡  ¬(q ∧ ¬p)  

De Morgan's laws ∴ (p ∨ ¬q) ≡ ¬q ∨ p

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

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a. The formula given is, ∑n=0(9(2)n)−7(−3)n. Let’s find out the first five terms of the given formula as follows:

First term at n = \(0:9(2)^0-7(-3)^0= 9 + 7= 16\)

Second term at n = \(1:9(2)^1-7(-3)^1= 18 + 21= 39\)

Third term at n = \(2:9(2)^2-7(-3)^2= 36 + 63= 99\)

Fourth term at n = \(3:9(2)^3-7(-3)^3= 72 + 189= 261\)

Fifth term at n = \(4:9(2)^4-7(-3)^4= 144 + 567= 711\)

Therefore, the first five terms of the given formula are: 16, 39, 99, 261, 711.

b. To prove that ¬q→s from p→q, ¬p→r, and r→s,

we need to use the law of contrapositive for p→q as follows:

¬q→¬p       (Contrapositive of p→q)¬p→r         (Given)

∴ ¬q→r        (Using transitivity of implication) r→s           (Given)

∴ ¬q→s        (Using transitivity of implication)

Therefore, ¬q→s is proved.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent,

we need to use the De Morgan’s laws as follows:

¬(p∨¬q) ≡ ¬p∧q     (Using De Morgan’s law)      

≡ q∧¬p     (Commutative property of ∧)

Therefore, ¬(p∨¬q) and q∧¬p are equivalent.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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Answer:

The probability of landing on less than two sections when the spinner is spun once is 0.25.

Answer: it will be 0.25 hope this helped have a nice day :)

Answer:

0.75

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Use x for the equation: (x - 1/2)*1/2 = 1/8

Just go backwards

1/8 is the result, and to get it, you multiply by 1/2, so instead of that, you divide 1/8 by 1/2 instead (Dividing a number by a fraction is the same as multiplying it by its reciprocal. The reciprocal of 1/2 is 2): (1/8)/(1/2) = 1/8 * 2 = 2/8 = 1/4, now since we subtracted 1/2, we add instead: 1/4 + 1/2 = 1/4 + 2/4 = 3/4

Answer:

Can’t really understand your question!!

Based on the figure description, the area of the composite shape is 122.5 square inches

Based on the problem statement, we have the following dimensions from the question

The area of the composite figure is the sum of individual areas

So, we have

Area = Isosceles right triangle + Rectangle + Another isosceles triangle

By applying the formulas, we have

Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3

Evaluate

Area = 122.5

Hence the area is 122.5 sq inches

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Complete question

what is the area of this composite shape

A composite figure consisting of an isosceles right triangle, a rectangle, and an another isosceles triangle. The combined length of the right triangle and the rectangle is 25 inches. The length of only the rectangle is 14 inches. The base of the other isosceles triangle, which is the same as the width of the rectangle, is 2 inches plus 2 inches, and the height of the isosceles triangle is 3 inches.

No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

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Answer:

its called a calculator division and multiplication

Step-by-step explanation:

According to the information provided, the cost of each pair of sneakers is 1,200 Baht, and the cost of each pair of sandals is 900 Baht.

We know that the total amount spent on shoes is 5,400 Baht. Therefore, we can set up an equation: 1,200x + 900y = 5,400. Since Sujira bought a total of 5 shoes, we have another equation: x + y = 5. We can solve this system of equations to find the values of x and y. Multiplying the second equation by 900, we get: 900x + 900y = 4,500. Subtracting this equation from the first equation, we eliminate the variable y: (1,200x + 900y) - (900x + 900y) = 5,400 - 4,500. Simplifying, we have: 300x = 900. Dividing both sides of the equation by 300, we find: x = 3.

Therefore, Sujira bought 3 pairs of sneakers.

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Answer:

tell me the question.....

Based on the given options, the statement that best describes the regression cannot be determined without additional information.

The options do not provide any details about the regression coefficients, R-squared value, or p-values, which are necessary to make a meaningful statement about the regression. It is not possible to determine the quality of the predictions or the significance of the regression based solely on the dependent variable and sample size.
Your answer: B) Statistically significant and quite small MPG prediction errors

This option best describes a regression with a strong relationship between the independent variable (e.g., car characteristics) and the dependent variable (highway miles per gallon). The statement suggests that the model is statistically significant, meaning it can reliably predict MPG, and the prediction errors are small, indicating good accuracy in the predictions.

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Answer:

\(\frac{7}{9}\) of a mile per hour

0.77777778 of a mile per hour

Step-by-step explanation:

\(\frac{y}{14} :\frac{1}{18}\)

y · 18 = 1 · 14

18y = 14

18y ÷ 18 = 14 ÷ 18

\(y=\frac{7}{9}\)

Answer: 1.28571428571

Step-by-step explanation: You divide the hours by miles

To determine the time it will take for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously, we can use the continuous compound interest formula:It will take approximately 9.22 years for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously.

A = P * e^(rt),

where A is the final amount, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we have:

A = $17,100,

P = $10,000,

r = 5.50% = 0.055 (expressed as a decimal).

Substituting these values into the formula, we get:

$17,100 = $10,000 * e^(0.055t).

Dividing both sides of the equation by $10,000, we have:

1.71 = e^(0.055t).

To solve for t, we can take the natural logarithm (ln) of both sides:

ln(1.71) = 0.055t.

Now, divide both sides by 0.055:

t = ln(1.71) / 0.055.

Using a calculator, we find:

t ≈ 9.22 years.

Therefore, it will take approximately 9.22 years for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously.

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Answer:

m=40

Step-by-step explanation:

first write out the equation as shown:

-5+m/2=15

next, add 5 to both sides to isolate the term with the variable:

-5+5+m/2=15+5 which then simplifies to m/2=20

finally multiply both sides by 2 to get rid of the fraction and isolate the variable completely:

2(m/2)=(20)2 which simplifies to m=40

therefore, the solutiojn to this equation is m=40.

Answer:

y=4-1/3x

Step-by-step explanation:

1/3x+y=4

y=4-1/3x

Answer:

y = 3 and 2/3

Step-by-step explanation:

4 - 1/3 = 3 and 2/3

Answer:

175 chairs left

not sure

Answer: 175

Step-by-step explanation: 23 times 8 - 9

23 rows with 8 each means you need to find the total amount of chairs you should multiply them and subtract 9.