The sat exams are scaled so that scores should roughly follow the normal distribution with mean 500 and standard deviation 100.how high must a student score on the sat mathematics exam to fall in the top 25% of all scores?

Answer:

16 and -16

Step-by-step explanation:

Answer: D. 16 and -16

Step-by-step explanation: I dont think you need an explanation because it is multiple choice.

Taking into account the definition of a system of linear equations, a small pizza and a regular pizza cost £7 and £11 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This mieans thar systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

2r + 3s= 43

8r + 9s= 151

Of the several methods to solve a system of equations. it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "r" from the first equation:

2r= 43 - 3s

r= (43 -3s)÷2

r= 43/2 - 3/2s

Replacing this expression in the second equation:

8×(43/2 - 3/2s) + 9s= 151

Solving:

8×43/2 - 8×3/2s + 9s= 151

172 -12s + 9s= 151

-12s + 9s= 151 - 172

-3s= -21

s= (-21)÷ (-3)

s= 7

Remembering that r=43/2 - 3/2s you get:

r=43/2 - 3/2×7

r= 11

Finally, a small pizza cost £7 and a regular pizza cost £11.

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a) Jeffrey needs an extra amount of $40,357.5 for buying a car.

b) After 20 years fund is worth $1364.

c) After 20 years $1200 interest had been earned.

a) P = $500

r = 12% = 12 ÷ 100 = 0.12

n = 12 because it was compounded 12 times in a year.

t = 5 years

Therefore,

A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]

A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]

A = 500 × 1.285

A = $ 642.5

Jeffrey needs an extra $40,357.5 for buying a car.

b) P = $500

r = 12% = 12 ÷ 100 = 0.12

n = 12 because it was compounded 12 times in a year.

t = 20 years

Therefore,

A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]

A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]

A = 500 × 2.728

A = $1364

After 20 years fund is worth $1364.

c) Simple interest = P × R × T ÷ 100

Simple interest = 500 × 12 × 20 ÷ 100

Simple interest = $1200

After 20 years $1200 interest had been earned.

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The features of the triangle are summarized below:

In this problem we find the case of a triangle whose three sides (AB, AC, BC) are known. First, we rationalize the expression for AC, that is, eliminate the irrational denominator by algebraic means:

AC = 1 / (√7 - √6)

AC = [1 / (√7 - √6)] · [(√7 + √6) / (√7 + √6)]

AC = (√7 + √6) / [(√7 - √6) · (√7 + √6)]

AC = (√7 + √6) / (7 - 6)

AC = √7 + √6

Second, we determine the square of each side:

AB² = (√7 + √6)²

AB² = 7 + 2√42 + 6

AB² = 13 + 2√42

AC² = (√7 + √6)

AC² = 13 + 2√42

BC² = (√14 + 2√3)²

BC² = 14 + 4√42 + 12

BC² = 26 + 4√42

BC² = 2 · (13 + 2√42)

BC² = 2 · AB² = 2 · AC²

Third, deduce the nature of the triangle:

Since BC = √2 · AB = √2 · AC, then the triangle ABC is a right triangle with internal angles 45° - 45° - 90°.

Fourth, calculate the area of the triangle by Heron's formula:

s = 0.5 · (AB + AC + BC)

s = 0.5 · (√7 + √6 + √7 + √6 + √14 + 2√3)

s = 0.5 · (2√7 + 2√6 + √14 + 2√3)

s = √7 + √6 + 0.5√14 + √3

A = √[s · (s - AB) · (s - AC) · (s - BC)]

A = √[(√7 + √6 + 0.5√14 + √3) · (√7 + √6 + 0.5√14 + √3 - √7 - √6) · (√7 + √6 + 0.5√14 + √3 - √7 - √6) · (√7 + √6 + 0.5√14 + √3 - √14 - 2√3)]

A = √[(√7 + √6 + 0.5√14 + √3) · (0.5√14 + √3) · (0.5√14 + √3) · (√7 + √6 - 0.5√14 - √3)]

A = √[8.698 · (8.698 - 5.095) · (8.698 - 5.095) · (8.698 - 7.206)]

A = √(8.698 · 3.603² · 1.492)

A ≈ 12.980

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Answer: Yes, 6.20

Step-by-step explanation:

1/5 is equal to 0.20, so 6 1/5 equals 6.20

The greatest common factor of the given terms is 2a⁴b

From the question, we are to determine the greatest common factors of the given terms

The given terms are

18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7

That is,

18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷

We will express each of the given terms as a product of their factors

18a⁴b⁹c² = 2 × 3 × 3 × a⁴ × b⁸ × b × c²

34a⁶b⁵ = 2 × 17 × a⁴ × a² × b⁴ × b

22a⁸bc⁷ = 2 × 11 × a⁴ × a⁴ × b × c⁷

Hence, the GCF is 2 × a⁴ × b = 2a⁴b

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Answer:x squared = 60

Step-by-step explanation:

x2-6=54, first you have to cancel out the 6 on the left side by adding 6 to -6 after doing that you are left with

x2-(-6+6)=54

but since you did +6 on the right side you have to do +6 on the left so after that you are left with

x2=54+6

now you just do 54+6=60 so after all of that you get

x2=60

(you can use a calculator to find the square root of 60)

Just take off the "S" from Seven.

"Even" is formed.

Just take the "S" out of Seven. It becomes "even."

An even number is one that divides by two and leaves a 0 as the final result.

2, 4, 6, 8, 10, and other even numbers are examples.

To really make 7 an even number, add 1.

7 + 1 = 8

It becomes 8, which is even.

Another way to make it even is to subtract 1.

7 - 1 = 6

It becomes 6, which is even.

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When a transversal crosses parallel lines corresponding angles are congruent.

What are corresponding angles?

Two lines are parallel if and only if the two angles of any pair of transversal corresponding angles are congruent (equal in measure). Proposition 1.28 of Euclid's Elements, an absolute geometry theorem (therefore true in both hyperbolic and Euclidean Geometry), demonstrates that if the angles of two transversals are corresponding, the two lines are parallel (non-intersecting). According to Euclid's parallel postulate, if two lines are parallel, the angles of a pair of corresponding angles are congruent (Proposition 1.29 of Euclid's Elements). If the angles of one pair of related angles are congruent, the angles of the remaining pairs are likewise congruent.

The correct option is (D) When a transversal crosses parallel lines corresponding angles are congruent.

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Duncan's height is the closest to the mean for the given normal distribution.

We learn from the question that

Given that 3-year-old boys' heights are roughly normally distributed, the mean will be the 50th.

Thus, comparing Duncan's height in the 32th percentile and Shane's height in the 62nd percentile with the mean height in the percentile 50.

i.e

50 - 32 = 18

and

62 - 50 = 12

Duncan's height is the closest to the mean.

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The complete question is -

The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3 year old boys. Duncan is 32.0 inches tall and is in the 32nd percentile. Shane is 34.0 inches tall and is at the 62nd percentile. Which is the closest to the mean

Answer:

the fraction is 2/5

Step-by-step explanation:

4/5 + 1/2

=2/5

The coordinate B are (-2, -6)

Given that, the coordinates of the midpoint of line segment AB are (3,-1). Also, coordinates of A are (8,4).

Let the coordinates of B be (a,b)

We know that,

Midpoint of two points (x1,y1) and (x2,y2) is  calculated by the formula

          [tex]\frac{x1+x2}{2} ,\frac{y1+y2}{2}[/tex]

Hence, midpoint of AB= [tex]\frac{8+a}{2} ,\frac{4+b}2}[/tex] = (3,-1)

                              [tex]\frac{8+a}{2}= 3 ,\frac{4+b}2} = -1[/tex]

                               8+a = 6,  4+b= -2

                                    a = -2  b = -6

             Hence the coordinate B are  (-2, -6)

In geometry, a centroid is the mid point of a  segment. It is equidistant from both endpoints and  is the mid point of both  the segment and  the endpoints. This divides the segment into two.

mid point can be calculated by    [tex]\frac{A+B}{2}[/tex]  

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Answer:

870,000

Step-by-step explanation:

Ten thousand is 10,000.

The ten thousand value here is 6

The thousand value here is 7.

Using rounding rules, 5 and up goes up therefore the ten thousand value becomes 7.

867,000 --> 870,000

Hope that helps

Answer: 1665

Step-by-step explanation:

Prime factorization of the numbers:

15 = 3 × 5

45 = 3 × 3 × 5

37 = 37

LCM(15, 45, 37)

= 3 × 3 × 5 × 37

= 1665

Hope this helps!

Answer: 2.5.02

Step-by-step explanation:

Answer: r

Step-by-step explanation:

The figures are symmetrical about line r.

Answer:

[tex]f(x)=x^4(x-a)(x-b)^2[/tex]

Step-by-step explanation:

The graph of a polynomial function will:

The zero at the origin (0, 0) touches the x-axis and so it has an even multiplicity (exponent).  Therefore, we can immediately discount the first two answer options as both have x as a zero (x = x¹ so its exponent is odd).

The end behavior of the graphed function means the leading coefficient is positive and the degree of the polynomial is odd.

The sum of the multiplicities is the degree of the polynomial function.

[tex]f(x)=x^4(x-a)(x-b)^2 \implies \textsf{Sum of multiplicities}: 4+1+2=7[/tex]

[tex]f(x)=x^2(x-a)^5(x-b) \implies \textsf{Sum of multiplicities}: 2+5+1=8[/tex]

Therefore, the only function that could represent the given graph is

[tex]\boxed{f(x)=x^4(x-a)(x-b)^2}[/tex]

as its degree is odd and it has a zero at the origin with even multiplicity.

Answer:

2. 14.42

3. 17.69

6. 12.8

9. 10.29 (I cant see your answer)

Rest is correct ;D

Step-by-step explanation:

The linear function that represents the profit earned is: C. y = 2x − 48.

The linear Function can be written as y = mx + b, which is in slope-intercept form, where we have:

From the information given, we have:

x = number of hot dogs sold

y = Profit earned

m = unit rate = 2

b = starting value = -48 (this is negative because the profit on each hot dog sold must be deducted from the cost for each morning.)

Therefore, substitute m = 2 and b = -48 into y = mx + b to write the linear function:

y = 2x - 48

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Answer:

C

Step-by-step explanation:

i said so

Answer:

Step-by-step explanation:

(12 nights)($184) = $2208

(9 nights)($6) = $54

(6 taxi rides)($27) = $162

$2208 + $54 + $162 = $2424

We will use a ratio to calculate American dollars to pounds

2424/x = 1.83/1

Cross multiply

1.83x=2424

Divide

= ~£1324.59

£1324.59 + £1600 = £2924.59

The answer is ~2924.59 pounds

The total cost of the flights, the hotel room, the wifi, and 6 taxi journeys for Tony's holiday in Canada is approximately £2925.13.

Given that Tony is vacationing in Canada, his flight cost is £1600, he stayed for 12 nights, his hotel cost $184 per night, Tony used wifi for 9 days. Wifi cost $6 per day. Tony took a taxi 6 times costing a mean average of $27 per taxi journey.

The exchange rate was $1.83 to £1.

We need to find the total cost his spend in the vacation.

To calculate the total cost of Tony's holiday, we need to convert all the expenses to pounds and then sum them up.

Flights cost: £1600

Hotel cost per night: $184

Hotel cost for 12 nights: 12 nights x $184/night = $2208

Wifi cost per day: $6

Wifi cost for 9 days: 9 days x $6/day = $54

Taxi cost per journey (mean average): $27

Total taxi cost for 6 journeys: 6 journeys x $27/journey = $162

Now, we need to convert the costs from dollars to pounds using the exchange rate of $1.83 to £1.

Flights cost in pounds: £1600

Hotel cost in pounds: $2208 / $1.83 = £1207.10

Wifi cost in pounds: $54 / $1.83 = £29.51

Taxi cost in pounds: $162 / $1.83 = £88.52

Finally, we can calculate the total cost in pounds:

Total cost = Flights cost + Hotel cost + Wifi cost + Taxi cost

Total cost = £1600 + £1207.10 + £29.51 + £88.52

Total cost = £2925.13

So, the total cost for Tony's holiday in Canada is approximately £2925.13.

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The reasons that proves the congruency of the triangles are;

2.7 [tex] \Delta EDF \cong \Delta FGE[/tex] by SSS congruency postulate

2.8 [tex] \Delta AOB \cong \Delta COB[/tex], by SAS congruency rule

[tex] \Delta AOB \cong \Delta COB[/tex], by ASA congruency rule or postulate

The rules that proves two triangles to be congruent is if they satisfy any of the 5 rules of congruency, which are; Side–side–side, or SSS, side–angle–side, or SAS, side–angle–angle, or SAA, angle–side–angle, or ASA, and right angle–hypotenuse–side, or RHS

2.7 The given parameters of the two triangles are;

DE = GF, and DF = GE

Required;

To prove that

[tex] \Delta EDF \cong \Delta FGE[/tex]

Solution;

From the given diagram, we have;

[tex]EF \cong FE[/tex]

Reflexive property

Therefore;

[tex] \Delta EDF \cong \Delta FGE[/tex]

Side–Side–Side, SSS rule of congruency

The Side–Side–Side congruency postulate states that if the three sides of one triangle are congruent to three sides of another triangle, then both triangles are congruent.

2.8 The circle information are;

The midpoint (center) of the circle = Point O

Segment OB is perpendicular to segment AC, [tex] OB \perp AC [/tex]

OB bisects AC

Required;

To prove that [tex] \Delta AOB \cong \Delta COB[/tex]

Solution;

Segment OA and OC are the radius of circle O

Therefore;

[tex] OA \cong OC[/tex] by the properties of the radius of a circle

The angle [tex] \angle OAB \cong \angle OCB [/tex] ; Base angles of isosceles triangle ∆OAC

[tex] AB \cong BC[/tex], Segments formed by the perpendicular bisector OB

Given that AB, [tex] \angle OAB [/tex] and OA in [tex] \Delta AOB [/tex] are congruent to BC, [tex] \angle OCB [/tex] and OB in [tex] \Delta COB [/tex], we have;

Second proof;

Given that OB is the perpendicular bisector of AC, we have;

[tex] \angle OBA \cong \angle OBC = 90^{\circ} [/tex], definition of angles formed by perpendicular lines

[tex] AB \cong BC[/tex]

Therefore;

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Answer:

The rectangles length is 2 times as much as its width.

Step-by-step explanation:

8 x 10⁴ = 80,000

4 x 10⁴ = 40,000

40,000 x 2 = 80,000

The number of steel beam the truck can carry  given the truck's  capacity is 182.37.

In order to determine the number of steel beam the truck can carry divide the capacity of the truck by the weight of each steel beam.

Division is the mathematical operation that is used to group a number into equal parts using another number. The sign used to denote division is ÷. Other operations used in mathematics are addition, subtraction and multiplication.

Number of steel beams the truck can carry = capacity of the truck / number of steel beams

6,000 / 32.9 = 182.37

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Answer:

I think the first number is 45 and the second number is 81.

Step-by-step explanation:

45 > 42 but 45 < 55       81 > 80 but 81 < 89

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products.

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products. A factored form can represent any logic function, and every factored form represents some logic function.

1a)The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)Area = length × width

To estimate the algebraic expressions for length and width

Area = (7x + 3)(4x - 2) = 28x² - 14x + 12x - 6 = 28x² - 2x - 6

Area = 28x² - 2x - 6

Given x = 10,

Let the equation be 28 x² - 2x - 6

substitute the value of x, in the above equation, we get

= 28(10)² - 2(10) - 6

= 2774

Area = 2774 sq . m

2. We can group the first two terms and next two terms:

xy - 4y + 7x - 28 = (xy - 4y) + (7x - 28)

simplifying the above equation, we get

y(x - 4) + 7(x - 4) = (x - 4)(y + 7)

Therefore, the equation is in factored form.

The complete question is:

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow change. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length that is three more than seven times x and the width is four times x minus 2.a.) What are the dimensions of your mowing plot? (2 points)

Length: ______________________________________

Width: ______________________________________

b.) What is the area of your plot (remember area = length x width)? (2 points)

Area: _________________________________________

c.) If x = 10 meters, how many square meters is your plot? (show steps)(2 points)

Area: _________________________________________

2.) Factor by grouping: (4 points)

xy − 4y + 7x − 28

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The bonus based upon the given formula is $2606.15 approximately

Given,

Annual salary = $48,000

Yearly sales = $76,000

Bonus is given according to the formula:

2 weeks salary + 1 percentage commission

Here,

Annual salary is given as $48,000

We have to find the weekly salary:

There is 52 weeks in a year.

So, salary for one week = Annual salary / number of weeks =  48000/52 = $923.077

Now, salary for two weeks = 923.077 × 2 = $1846.154

Rate of annual commission is 1%

The commission amount:

1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760

So,

The bonus amount = 2 weeks salary + 1 percentage commission

The bonus amount = 1846.154 + 760

The bonus amount = 2606.154

Therefore, the bonus given based upon the given formula is $2606.154

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