pls help im running out of time

Answer:

Step-by-step explanation:

Let the number = x

x^2 = 2*x + 7         Subtract 2x + 7 from both sides

x^2 - 2x - 7 = 0

a = 1

b = -2

c = - 7

x = (-b +/- sqrt(b^2 - 4ac))/2a     General Formula

x =  (-(-2) +/- sqrt((-2)^2 - 4*1*(-7))/2          Values substituted

x = (2 +/- sqrt(4 + 28))/2                            Combine the square root

x = (2 +/- sqrt(32))/2                                   sqrt(32) = sqrt(4*4*2) = 4sqrt(2)  

x = (2 +/- 4sqrt(2)) /2                                  Divide by 2

x = 1 + 2*sqrt(2)

Let x represent the "smallest number" of a set of three unknown numbers.

• The greatest os 4 times the smallest, symbolically: 4x

• The middle number is three more than the smalles, symbolically x+3

• The sum of the smallest and the greatest is the same as 2 times the middle number, symbolically: x+4x=2(x+3)

Using the last expression you can clear the value of x (the smallest number)

x=2 → The smallest number of the set of three is 2

Now using this value and the given equivalencies we can calculate the midle and greatest number:

Middle number

x+3= 2+3= 5

Greatest number

4x=4*2=8

The set of three numbers is (2, 5, 8)

The general equation of a circle is

Here, (h,k) is the center of the circle and r is the radius of the circle.

change the given equation into the general form as follows:

So, the center is (0,0) and the radius is r = 5.

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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Answer:

m = 3

Step-by-step explanation:

5 + 2m = 11 ( subtract 5 from both sides )

2m = 6 ( divide both sides by 2 )

m = 3

\(\huge\mathfrak{\underline{Answer:}}\)

❒ The length of longest side of first Trianlge :

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ\(\large\bf{32\:cm}\)

__________________________________________

\(\large\bf{\underline{given:}}\)

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\bf A$}\put(0.5,-0.3){$\bf C$}\put(5.2,-0.3){$\bf B$}\end{picture}\)

\(\setlength{\unitlength}{0.75 cm}\begin{picture}(0,1)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\bf P$}\put(0.5,-0.3){$\bf R$}\put(5.2,-0.3){$\bf Q$}\end{picture}\)

__________________________________________

\(\large\bf{\underline{To \:find :}}\)

__________________________________________

\(\large\bf{\underline{Perimeter\:of\: second\: triangle:}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=sum\:of\:all\:sides}\)

‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=4.5+6+8}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=18.5}\)

❒ The ratio between the perimeter of two triangles :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=\frac{perimeter\:of\:1st\: triangle}{perimeter\:of\:2nd\: triangle}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=\frac{74}{18.5}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=4:1}\)

❒ The two triangles are similar , therefore the ratio of their sides will also be similar , i.e 4:1

➽ Let the sides of first Trianlge be x , y and z

\(\large\bf{\underline{Therefore:}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹\frac{x}{4.5}=\frac{4}{1}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹\frac{y}{6}=\frac{4}{1}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹\frac{z}{8}=\frac{4}{1}}\)

\(\large\bf{\underline{Hence:}}\)

❒ Length of first side :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹\frac{x}{4.5}=\frac{4}{1}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹x=4\times 4.5}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹x=18}\)

❒ Length of second side :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹\frac{y}{6}=\frac{4}{1}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹y=4\times 6}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹y=24}\)

❒ Length of third side :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹\frac{z}{8}=\frac{4}{1}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹z=4\times 8}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹z=32}\)

__________________________________________

\(\large\mathfrak{Length\:of\: largest\:side:}\)

\(\huge\bf{=32cm}\)

Answer:

Only Carla

Step-by-step explanation:

Its the right way to solve (x+1)(x-1)=8

Answer:

Only Carla's

Step-by-step explanation:

Khan

Applying the Pythagoras Theorem, the length of RS = 8 units.

According to the figure,

Diameter = 16 +4 = 20 units

So, the Radius = Diameter/2 = 20/2 = 10 units

Now,

Let the center be M, then

MT = 10 - 4 = 6 units

RT = x units

The radius is perpendicular to the chord,

So, MTR will be a right-angled triangle,

We will apply the Pythagoras theorem,

So, we have :

\(RT^{2} +TM^{2} =RM^{2}\)

Here, RT = x units

TM = 6 units and RM = radius = 10 units

Putting these values in the Pythagoras theorem,

\(x^{2} +6^{2} =10^{2}\\x^{2} + 36 = 100 \\x^{2} = 100 - 36 = 64\\x^{2} = 64 \\x = 8\)

Thus, the length of RS = 8 units.

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\(\huge{ \mathcal{  \underline{ Answer }\:  \:  ✓ }}\)

According to the unit circle, the value of sin will be :

\( \boxed{\boxed{\longrightarrow \dfrac{ - \sqrt{3} }{2} }}\)

Since, value of sin\((\theta)\) is always negative in the fourth quadrant, therefore it can't be \(\dfrac{1}{2}\).

_____________________________

\(\mathrm{ ☠ \: TeeNForeveR \:☠ }\)

Answer:

$3.80/pound

Step-by-step explanation:

We can just divide the price by the amount to find the price per pound.

20.90 ÷ 5.5 = 3.80

Hope this helps!

Answer:

Credit (C) = $45.50 - 0.10x

Step-by-step explanation:

Since you are wanting the credit (C) that is the y variable.

The prepaid phone card starts off with a balance of $45.50.

Every minute a call is made $0.10 is deducted (subtracted) from the card.

The unknown number or 'x' represents the number of minutes the calls lasted.

Answer:

4

Step-by-step explanation:

Answer:

5,14

Step-by-step explanation:

The function of the town's population is an exponential growth

From the question, we have the following parameters that can be used in our computation:

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula. In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\frac{X-\mu}{\sigma}\)

How long must a visit be to put a shopper in the longest 20 percent?

Here \(\mu=41.8 , \sigma=17.3\)

The 100-20=80th percentile, which is X when Z has p-value of 0.8, so Z=0.84

\(Z=\frac{X-\mu}{\sigma}\)

\(0.84=\frac{X-41.8}{17.3}\)

14.532=X-41.8

X=14.532+41.8

X=56.33

A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.

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Only (d) 1 equation can you write to represent a single line using a point-slope equations

From the question, we have the following parameters that can be used in our computation:

Equation = Linear equation

A linear equation can only be represented with one equation

When it is represented with multiple equations, the equations are equivalent equations

This means that the equations can be converted to one another

Hence, the solution is (d) 1 equation

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Answer:

square root of 2 times square root of 3

2.44

Answer:

Step-by-step explanation:

Given the expressions :

The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.

Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.

Let the original price = x

Expression 1 : The list price of the item is 80 percent of the original price

List price = 80% of x

List price = 0.8x

Expression 2: The price of the item has been reduced by 80 percent

Price = x - 80% of x

Price = x - 0.8x

Price = 0.2x

Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.

Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.

Answer:

4

Step-by-step explanation:

because 60/15 is 4

Assuming that the order of the cities matters, the number of possible routes is 11! (11 factorial), which is 39916800.

The number of possible routes for an overnight express company that includes eleven cities on its route is 39916800. This is because when the order of the cities matters, the number of possible routes can be calculated by finding 11 factorial, which is:

This calculation results in 39916800, which means that there are 39916800 potential routes for an overnight express company with eleven cities on its route.

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Answer:

X > (greater than or equal to) -7

Step-by-step explanation:

3x + 15 > -6

3x > -21 (subtract 15 from both sides)

X > -7 (divide both sides by 3)

The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

Answer:

The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

9 ± √89 /4 = 2x² - 9x - 1.

4 ± √22 /2 = 2x² - 8x - 3.

Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5.                                                  x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4.     24 can also be written as 4 × 6 and √4 = 2. So                                                                                     x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3.                                                   x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So                                                                              x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3.                                                    x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4.     88 can also be written as 4 × 22 and √4 = 2. So                                                                             x = 8 ± 2√22 / 2×2 = 4± √22/2.

2x² - 9x - 1, here a = 2, b = -9, c = -1.                                                     x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4.                                          x = 9 ± √89 / 4.

2x² - 9x + 6, here a = 2, b = -9, c = 6.                                                    x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4.                                                                             x = 9 ± √33 / 4 .

Answer: 2⁵

Explanation: Since these two powers have the same base of 2,

you can multiply them together by simply adding their exponents.

When we do that, we get 2⁵.

A common mistake in this problem would be to multiply

the bases together and give an answer of 4⁵.

The 2's can't be multiplied together however because

they are  not coefficients, they are bases.

When applying your exponent rules, your base will never change.

There are 1260 different strings that can be made from 5 of the 7 letters in the word "meeting."

To determine the number of unique subsets of 5 letters from the word "meeting," we can use the combination formula:

\(n_Cr = n! / r!(n-r)!\)

Where n is the total number of items (in this case, the number of letters in the word "meeting") and r is the number of items being selected (in this case, 5 letters).

So, for "meeting," n = 7 and r = 5.

Plugging these values into the formula gives:

\(7C5 = 7! / 5!(7-5)! = 21\)

Therefore, there are 21 unique subsets of 5 letters that can be formed from the letters in the word "meeting."

To determine the number of different strings that can be made from 5 of those 7 letters, we can use the permutation formula:

\(n_Pr = n! / (n-r)!\)

Where n is the total number of items (in this case, the number of letters in the word "meeting") and r is the number of items being selected (in this case, 5 letters).

So, for "meeting," n = 7 and r = 5.

Plugging these values into the formula gives:

7P5 = 7! / (7-5)!

= 7! / 2!

= 2520 / 2

= 1260

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Cylinder A can hold 6902.08 ft^3

Cylinder B can hold 5654.87 ft^3

6902.08 - 5654.87 = 1247.21

The amount that will be left over in container A is 1247.21

Answer:

B

Step-by-step explanation:

Answer:

  15 batches

Step-by-step explanation:

To find the number of batches, divide the available flour by the amount used per batch.

  (10 c)/(2/3 c/batch) = 10×3/2 batches = 15 batches

Jess can make 15 batches of tarts with her 10 cups of flour.

Answer:

Step-by-step explanation:

Make proportions:

Cross-multiply and solve for x:

Answer:

F can be at 19 or -5

Step-by-step explanation:

If F is on positive number line, F-E=12

F=12+7=19

If F is on negative number line, E-F=12

-F=12-7=5, F=-5

System of inequalities that represents this scenario is 7x + 11y ≥ 700 (the total amount of merchandise sold must be at least $700) y ≥ 50 (at least 50 coffee mugs must be sold)

Dominique is selling merchandise for a school fundraiser. To meet her goals, she must sell at least $700 worth of merchandise, including at least 50 coffee mugs.

Let x be the number of calendars sold and y be the number of coffee mugs sold. The revenue from selling x calendars and y coffee mugs can be calculated as follows:

Revenue = (Price per calendar) x (Number of calendars sold) + (Price per coffee mug) x (Number of coffee mugs sold)

Given that calendars are being sold for $7 each and coffee mugs are being sold for $11 each, the revenue equation can be expressed as:

Revenue = 7x + 11y

To meet the fundraising goal of selling at least $700 worth of merchandise, the total revenue generated from the sale of calendars and coffee mugs must be at least $700. Hence, we can express this as the inequality:

7x + 11y ≥ 700

In addition, Dominique must sell at least 50 coffee mugs. This can be expressed as the inequality:

y ≥ 50

Combining both inequalities, we get the system of inequalities:

7x + 11y ≥ 700 and y ≥ 50

This system of inequalities represents the scenario where Dominique must sell at least $700 worth of merchandise, including at least 50 coffee mugs. The first inequality ensures that the total revenue generated from the sale of calendars and coffee mugs meets the fundraising goal, while the second inequality ensures that at least 50 coffee mugs are sold.

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p(x) must be equal to (x-a)(x-b) where b is another number.

If p(a) = 0, then this implies that (x-a) is a factor of p(x). Therefore, p(x) can be factored into (x-a)q(x), where q(x) is a polynomial of degree one less than the degree of p. This means that p(x) must be equal to (x-a)(x-b) for some other number b. It does not mean that p(x) must be equal to the zero polynomial or (x-a)².

The product of two factors, (x-a) and (x-b), is a polynomial of degree two, p(x). This can be expressed in expanded form as p(x) = x² - (a + b)x + ab, where a and b are any two numbers

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