The Census Bureau says that the 10 most common surnames in the United States are, in order, Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Suppose you look at the authors of the textbooks for your current courses and find that there are 8 authors in total. What is the probability that none of the 8 surnames of these authors were among the 10 most common

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

Answer:

1. The critical value to be used for constructing the confidence interval is 1.415

2. The standard error of the sampling distribution to be used in constructing the confidence interval, is approximately 6.260

Step-by-step explanation:

The number of mail-order receipts, n₁ = 8 sales receipts

The mean amount of sale, \(\bar x_1\) = $69.30

The standard deviation of the sample, σ₁ = $26.25

The number of internet sales receipts, n₂ = 17 sales receipts

The mean amount of sale, \(\bar x_2\) = $75.90

The standard deviation of the sample, σ₂ = $28.25

1. Where the population variance are not equal, we have;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) - t_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}< \mu _{1}-\mu _{2}< \left (\bar{x}_1-\bar{x}_{2} \right ) + t_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}\)

Where;

\(t_c\) = The critical value for constructing the confidence interval

\(\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}\) = \(S.E_{\bar{x}_1-\bar{x}_{2}} =\) The standard error for constructing the confidence interval

The degrees of freedom, df = n₁ - 1 = 8 - 1 = 7

The t-value at 90% confidence level, and degrees of freedom of 7, \(t_{90\%, 7}\), from the tables is given as follows;

\(t_c\) = \(t_{90\%, \, 7}\) = 1.415

The critical value for constructing the confidence interval = \(t_c\) = 1.415

2. The standard error of the sampling distribution to be used in constructing the confidence interval, \(S.E._{\bar{x}_1-\bar{x}_{2}}\), is given as follows

\(S.E_{\bar{x}_1-\bar{x}_{2}} = \sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}\)

\(S.E._{\bar{x}_1-\bar{x}_{2}} = \sqrt{\dfrac{26.25^{2}}{8}-\dfrac{28.25^{2}}{17}} \approx 6.260\)

\(S.E._{\bar{x}_1-\bar{x}_{2}}\) ≈ 6.260

The standard error of the sampling distribution to be used in constructing the confidence interval, \(S.E._{\bar{x}_1-\bar{x}_{2}}\) ≈ 6.260

There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The function f(x) = x³ +7x² - 5x + 19 is a polynomial function of degree 3, which means it has 3 roots (also known as zeros or solutions) that could be real or complex.

To determine the number of negative real roots, we can use the fact that a cubic function has at least one real root.

x³ +7x² - 5x + 19

the first coefficient is positive, the second is positive, the third is negative, and the fourth is positive.

There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"

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Answer:

× = -4

or

× = 8

Step-by-step explanation:

because the gravity of the Earth

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Step-by-step explanation:

It's C

I hope it helped:)

The required angle is 35 degrees whose supplementary angle is 35 degrees more than twice its complementary angle.

The definition of a supplementary angle is that it adds up to 180 degrees.

Let's represent the required angle as "x".

We know that the supplementary angle to "x" is 180 - "x".

Similarly, the definition of a complementary angle is that it adds up to 90 degrees, so we know that the complementary angle to "x" is 90 - "x".

Given that the supplementary angle to "x" is 35 degrees more than twice its complementary angle, so we can write this as an equation:

180 - x = 2(90 - x) + 35

Simplifying this equation, we get:

180 - x = 180 - 2x + 35

Adding x to both sides, we get:

x = 35

Therefore, the required angle is 35 degrees.

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To find the volume of the triangular prism use the following formula:

Where B is the triangular base and h is the height of the prism.

Find the area of the triangular base by using the following formula:

Now, find the volume of the triangular prism:

It means that the volume of the prism is 450in^3.

People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

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Answer

a) It will take 3.54 years for the turtle population to hit 300 female turtles.

b) There will be 78,125 female turtles in 7 years.

Explanation

The model has been give to us as

T(t) = 5ᵗ

where

T(t) = Female turtle population at any time t

t = time in years

First part of the question asks us to find when the turtle population will hit 300 female turtles. That is, find t when T(t) = 300

T(t) = 5ᵗ

300 = 5ᵗ

We can rewrite this as

5ᵗ = 300

We will take the natural logarithms of both sides

In 5ᵗ = In 300

t (In 5) = In 300

t (1.6094) = 5.7038

Divide both sides by 1.6094

t = (5.7038/1.6094)

t = 3.54 years = 3 years, 6.5 months

For the second part of the question, we want to calculate the number of female turtles when t = 7 years

T(t) = 5ᵗ

T(7) = 5⁷ = 78,125 female turtles

Hope this Helps!!!

The number of pennies weighing as much s earth is  193 × 10²⁴

Index forms are described as described as those forms that are used to represent numbers that are too large or small in more proper ways.

Other names for index forms are scientific notation and standard forms.

Ratio is described as the comparison of numbers or variables on the basis of their size.

It shows how many times one number contains another.

From the information given, we have that;

The earth weighs = 5. 972 × 10 ²⁴ kilograms

The penny weighs = 3.1 × 10 ⁻³ kilograms

Divide the values

= 5. 972 × 10 ²⁴/3.1 × 10 ⁻³

= 1.93 × 10 ²⁶

= 193 × 10²⁴

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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Answer:

45

Step-by-step explanation:

30/2=15 +30=45

Answer:

The Jacobson Animal Shelter has 45 total animals.

Step-by-step explanation:

dogs = 30

cats = 30/2

cats = 15

dogs + cats = total

30 + 15 = total

45 = total

Answer:

(0, -2)

Step-by-step explanation:

Crosses the y-axis = find the y-intercept. Substitute x = 0 (if you draw a graph, you can see that the point where y crosses the y axis is always 0 for x) into the equation, and you get 3(0) - 7y = 14. Calculate, you get y = -2. Rewrite in coordinates form.

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

18 units

Step-by-step explanation:

5+5=10

4+4=8

8+10=18 units

Answer:

14

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of the 4 sides of a rectangle. Since in a rectangle opposite sides are congruent, you just need to find the lengths of any two adjacent sides because adjacent sides cannot be opposite. Then add them and multiply the sum be 2 to account for the opposites sides.

Two find the distance between any two points, you can use the distance formula. If the two points lie on the same vertical line (both points have the same x-coordinate), or if the two points lie on the same horizontal line (both points have the same y-coordinate), then just subtract the different coordinates and take the absolute value.

PQ = |2 - 6| = |-4| = 4

QR = |2 - 5| = |-3| = 3

perimeter = 2(length + width)

perimeter = 2(4 + 3)

perimeter = 2(7)

perimeter = 14

The zeros of g(x) = (x + 2)(x − 1)(x − 2) are x = -2, 1 and 2

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

The 5 functions of g(x)

To determine the key features of the function g(x), we make use of the first

g(x) = (x + 2)(x − 1)(x − 2)

So, we have

Zeros

This is when the function equals 0

(x + 2)(x − 1)(x − 2) = 0

Evaluate

x = -2, 1 and 2

The y-intercept

This is when the value of x in the function equals 0

g(0) = (0 + 2)(0 − 1)(0 − 2)

Evaluate

g(0) = 4

End behaviour

This is the behavior of the graph of the function as it approaches the ends of the x-axis

So, we have

\(\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:\)

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Answer:

Step-by-step explanation:

3x(2 1/5)= (6 3/5) * (x)

Answer:

6 3/5

Step-by-step explanation:

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Answer:

172

Step-by-step explanation:

Let adults be x

and children be y

According to the problem,

x + y = 348              . . . (1)

1.5x + 0.75y = $390. . . (2)

From Eq 1, find the value of x:

x = 348 - y

Put this value in Eq 2:

1.5 ( 348 - y ) + 0.75y = 390

522 - 1.5y + 0.75 y = 390

-1.5y + 0.75y = 390 - 522

-0.75y = -132

y= -132/-0.75

y = 176

Put the value of y in Eq 1

x  + 176 = 348

x = 348 -1 176

x = 172

No. of children = 176

No. of adults = 172

Recall that a ⇒ b   ⇔   ¬a ∨ b. So we can write

q ⇒ (p ∧ r )   ⇔   ¬q ∨ (p ∧ r )

Then the negation of this would be, for instance,

¬(¬q ∨ (p ∧ r ))   ⇔   ¬(¬q) ∧ ¬(p ∧ r )

…   ⇔   q ∧ (¬p ∨ ¬r )

…   ⇔   (¬p ∧ q) ∨ (q ∧ ¬r )

…   ⇔   ¬(p ∨ ¬q) ∨ (q ∧ ¬r )

…   ⇔   (p ∨ ¬q) ⇒ (q ∧ ¬r )

It's impossible to tell what kind of statement your program is expecting, but since there are 5 slots available, my money would be on q ∧ (¬p ∨ ¬r ), so long as ¬p and ¬r are options.

The area of the outer rectangle is 15 in²

The area of the smaller cut out rectangle is 2 in²

The area of the figure is 13 in².

Area is the region bounded by a plane shape.

To calculate the area of the shape, we use the formula below

Where:

Substitute these values into equation 2

Also,

To calculate the area of the smaller cut out rectangle, we use the formula below

Where:

Substitute these values into equation 2

Hence, the area of the figure is = 15-2 = 13 in²

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The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)

A vector is a physical quabntity thet has both magnitude and direction.

To find  the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows

Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),

Let A = (8, -6) and B = (-1, 5)

So, AB = B - A

= (-1, 5) - (8, -6)

= (-1 - 8), (5 - (-6))

= (-9, 5 + 6)

= (-9, 11)

So, the vector in component form is (-9, 11)

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Making a graph of linear inequalities is similar to making a graph of linear equations. But with inequalities, we find a region instead of a line.

What is linear inequality?

Linear inequalities are mathematical statements that are made up of two expressions which are compared using inequality symbols.

The following steps are to be followed to make a graph of linear inequality:-

1. Solve the inequality for y.

2. Considering the inequality as a linear equation graph the line. ( If the inequality sign does not contain an equal sign then draw a dashed line; if the inequality contains an equal sign then draw a solid line.

3. Shade the region that satisfies the inequality.

Hence, a system of linear inequality is graphed similarly to that of a linear equation, but a region is obtained.

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Mοst pοpular fοrm οf transpοrt fοr bοys is bicycle, Dual bar chart shοws the number οf students using different mοdes οf transpοrt tο schοοl.

a) Accοrding tο the data, the mοst pοpular fοrm οf transpοrt used by the bοys is the bicycle.

b)

Mοde οf transpοrt Bοys Girls

Car                        10         5

Bus                         8         6

Bicycle                  15         8

Walk                       7         5

c) The number οf students whο get tο schοοl by bus is 2 mοre than thοse whο get tο schοοl by car, sο the answer is 2.

d) The tοtal number οf students in Year 5 is 56. (10+5+8+7+8+6+15)

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Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

Answer:

6.91666666667

Step-by-step explanation: