Tyrell's SAT math score was in the 64th percentile. If all SAT math scores are normally distributed with a mean of 500 and a standard deviation of 100, what is Tyrell's math score? Round your answer to the nearest whole number

Answer:

[tex]\frac{13}{2}[/tex] square units

Step-by-step explanation:

We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).

We have to find the area of triangle.

We know that area of triangle=[tex]\frac{1}{2}\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid [/tex]

[tex]x_1=3,x_2=5,x_3=6[/tex]

[tex]y_1=1,y_2=4,y_3=-1[/tex]

Substitute the values in the formula then we get

Area of right triangle =[tex]\frac{1}{2}\mid (3(4+1)+5(-1-1)+6(1-4))\mid [/tex]

Area of right triangle =[tex]\frac{1}{2}\mid (15-10-18)\mid [/tex]

Area of right triangle =[tex]\frac{1}{2}\times 13=\frac{13}{2}[/tex] square units

Answer: the correct option is

C ​(x−4)(x+5)

Step-by-step explanation:

The area of the rug in square feet is expressed as

​x^2+x−20

The given equation is a quadratic equation and the roots of the equation represents the dimensions of the rug. To simplify the equation, we would apply the factorization method.

We will get two numbers such that, their difference will be x and their sum will be -20x^2. The numbers are 5x and 4x. Therefore

​x^2+ 5x - 4x −20 = 0

x(x + 5) - 4(x +5)

The roots are (x - 4)(x + 5)

The area of the rug is represented by the quadratic expression[tex]x^2 + x - 20,[/tex] which factors to (x + 4)(x - 5). This matches option A, verifying that these are the dimensions of the rug.

The student has a quadratic expression representing the area of a rug, which is[tex]x^2 + x - 20[/tex] square feet. To find the dimensions of the rug, we need to factor this expression. Factoring quadratic expressions involves finding two binomials that multiply to give the original quadratic expression. In this case, the correct factorization is (x + 4)(x - 5).

We can verify this by using the FOIL method (First, Outer, Inner, Last) to expand the binomials: (x + 4)(x - 5) = [tex]x^2 - 5x + 4x - 20 = x^2 - x - 20[/tex], which matches our original expression.

Thus, option A is the correct choice.

The question asks for the derivative of the function (2x+3)/(3x^2-4) at x=-1. Using the quotient rule, we find the derivative and then substitute x=-1 into it to get the required value.

The question aims to find the derivative of the function f(x) = (2x + 3) / (3x^2 - 4) and then find its value at x = -1. To do this, we need to use the Quotient Rule which is (f(x)/g(x))' = (g(x)*f'(x) - f(x)*g'(x))/(g(x))^2.

Here f(x) = 2x + 3 and g(x) = 3x^2 - 4. So, the derivative of the function becomes f'(x) = ( (3x^2 - 4)*2 - (2x + 3)*6x ) / (3x^2 - 4)^2 which simplifies to (6x^2 - 8 - 12x^2 - 18x) / ( 9x^4 - 24x^2 + 16). Now, substitute x = -1 into f'(x) to get the desired value.

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Answer:

[tex]1217+(4.1\times 10^3)=5.317\times 10^3[/tex]

Step-by-step explanation:

Given : Expression [tex]1217+(4.1\times 10^3)[/tex]

To find : After converting the following numbers into scientific notation, solve the problem ?

Solution :

Expression [tex]1217+(4.1\times 10^3)[/tex]

Re-write 1217 by multiplying and divide by 1000 to convert into decimal,

[tex]=\frac{1217\times 1000}{1000}+(4.1\times 10^3)[/tex]

[tex]=1.217\times 10^3+(4.1\times 10^3)[/tex]

[tex]=(1.217+4.1)\times 10^3[/tex]

[tex]=5.317\times 10^3[/tex]

Therefore, in scientific notation [tex]1217+(4.1\times 10^3)=5.317\times 10^3[/tex]

Answer:

C. $29.20

Step-by-step explanation:

The difference between using an electric stove and a gas stove everyday is 13 cents - 5 cents= 8 cents.

Saving 8 cents everyday.

Therefore for a year, Bryce will save 8 cents × 365days = 2920 cents

Then 2920 cents = $(2920÷100)

=$29.20

Answer:

C. $29.20

Step-by-step explanation:

Answer:

The y intercept of the equation is 10.

If it's 4 o'clock, the hour hand will be on the 4 and the minute hand will be on the 12.

This takes 4 partitions/pieces of the clock, and there are 12 different partitions. That's 4/12, or 1/3 of the entire clock.

The total clock is a 360 degree angle.

360 * (1/3) = 120

1/3 of 360 degrees is 120 degrees.

Since the angle between the minute and hour hand takes up 1/3 of the clock, the angle is 120 degrees.

Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

Triangle TML is similar to triangle TVU.  Side TV measures 36 and side TM meaures 9; side TV is 4 times longer than side TM.  Same with sides VU and ML.  VU is 4 times longer than ML.  That means that side TU is 4 times longer than side TL.  Side TL measures x - 4; side TU measures 24 + x - 4 which is x + 20.  That means that x + 20 = 4(x - 4) and x + 20 = 4x - 16 and

3x = 36 so

x = 12

Answer:x1 = 1, x2 = - 1, x3 = 3

Step-by-step explanation:

x1 + 2x2 - x3 = - 4 - - - - - - - - - -1

x1 + 2x2 + x3 = 2 - - - - - - - - - -2

- x1 - x2 + 2x3 = 6 - - - - - - - - - -3

Let us eliminate x1 and x2. Subtracting equation 2 from equation 1, it becomes

-2x3 = - 6

x3 = -6/-2

x3 = 3

Adding equation 2 to equation 3, it becomes

x2 + 3x3 = 8 - - - - - - - - - - - 4

Substituting x3 = 3 into equation 4, it becomes

x2 + 3 × 3 = 8

x2 + 9 = 8

x2 = 8 - 9 = -1

Substituting x2 = -1 and x3 = 3 into equation 2, it becomes

x1 + 2 × -1 + 3 = 2

x1 - 2 + 3 = 2

x1 + 1 = 2

x1 = 2 - 1 = 1

Let us check by substituting x1 = 1, x2 = -1 and x3 = 3 into equation 1. It becomes

1 + 2 × - 1 - 3 = - 4

1 - 2 - 3 = - 4

-1 - 3 = - 4

-4 = - 4

Answer:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

Step-by-step explanation:

We presume you're starting with ...

  y = ax^2 +bx +c

As you would with numbers, factor the first two terms:

  y = a(x^2 +b/a·x) +c

Add half the square of the x term inside and its opposite outside parentheses:

  y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2

  y = a(x +b/(2a))^2 +c -b^2/(4a)

You can combine the last two terms to a more familiar fraction:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

To write a quadratic function in vertex form, use the values of a, b, and c. Find the coordinates of the vertex using h = -b/2a and k = f(h).

Substitute the values into the vertex form.

To write a quadratic function in vertex form, you can use the values of a, b, and c.

The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k,

where (h, k) represents the coordinates of the vertex.

To find h and k, you can use the formulas h = -b/2a and k = f(h).

Once you have the values of h and k, you can substitute them into the vertex form to obtain the quadratic function in vertex form.

Learn more about quadratic function in vertex form here:

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Answer:

D

Step-by-step explanation:

Joe already has $40 and can save $20 each week. the total amount he can save in a given number of weeks is $20 multiplied by the that number of weeks which in this case is w so 20w. To find the total T of the amount he has after w weeks, you add the amount he already has to the amount saved. So the equation would be T=40+20w

Answer:

D) T = 40 + 20w

Step-by-step explanation:

Trust me! i had this on my test/ exam, and it was correct!!

i really hoped this helped! Have a wonderful day!

Answer:

1/12,000

Step-by-step explanation:

Data provided in the question:

Size of a population of mustard plants = 6,000

Now,

According to genetic drift theory

The probability that a newly-arisen mutation will become fixed is given using the formula

⇒ 1 ÷ [ 2 × Size of a population of mustard plants ]

⇒ 1 ÷ [ 2 ×6,000 ]

⇒ [ 1 ÷ 12,000 ]

Hence,

probability that a newly-arisen mutation will become fixed in this population is 1/12,000

The question is missing the figure. So, it is attached below.

Answer:

Area of the shaded sector is 144π units squared.

Step-by-step explanation:

Given:

Central angle of the sector is, [tex]\theta=\frac{8\pi}{9}\ rad[/tex]

Radius of the circle is, [tex]R=18\ units[/tex]

We know that, area of a sector of a circle of radius 'R' and central angle [tex]\theta[/tex] is given as:

[tex]A=\frac{1}{2}R^2\theta[/tex]

Plug in [tex]\theta=\frac{8\pi}{9},R=18[/tex]. This gives,

[tex]A=\frac{1}{2}\times (18)^2\times \frac{8\pi}{9}\\\\A=(\frac{324\times 4}{9})\pi\\\\A=(36\times 4)\pi\\\\A=144\pi\ units^2[/tex]

Therefore, the area of the shaded sector is 144π units squared.

Answer: 144Pi units squared

Step-by-step explanation:

Answer:

It is C

Step-by-step explanation:

(3x-2)(x+2)

3x(x)+3x(2)-2(x)-2(2)

3x^2+6x-2x-4

3x^2+4x-4 <----------

(Im bad at explaining but that is right trust me :P)

Answer:

  28 in²

Step-by-step explanation:

Without constraining the problem unduly, we can make the assumption that AB = 2 inches. Then the altitude from AB to D is h in ...

  Area ABD = (1/2)(AB)h

  16 in² = (1/2)(2 in)(h)

  16 in = h . . . . . . . . . . . divide by 1 in

__

The altitude D to AB is the sum of the heights from D to EC (h1) and from AB to EC (h2). That is ...

  16 = h1 + h2

We also know that the height from FG to EC is 1/2 the height from D to EC, hence (1/2)h1. Likewise, the height to midsegment HI from either EC or AB is half the height from EC to AB, hence (1/2)h2. This means the total height of the quadrilateral HFGI is (1/2)h1 + (1/2)h2 = (1/2)(h1 +h2) = 8.

__

We are given that FG is 50% longer than AB, so its length will be ...

  FG = AB×(1 + .5) = (2 in)(1.5) = 3 in

Since FG is the mid-segment of triangle CDE, base EC is twice its length, or ...

  EC = 2×FG = 2(3 in) = 6 in

__

Mid-segment HI is the average of the base lengths of trapezoid ABCE, so is ...

  HI = (EC +AB)/2 = (6 + 2)/2 = 4

__

Now, we know the height and base lengths of trapezoid HFGI, so we can find its area as ...

  A = (1/2)(b1 +b2)h = (1/2)(3 in + 4 in)(8 in) = 28 in²

The area of quadrilateral HFGI is 28 square inches.

_____

You can make any assumption you like about the dimension of AB, and the rest of the dimensions scale accordingly. The result is still the same.

Answer:

76

Step-by-step explanation:

Answer:

The 8th term of geometric sequence is -8748

ie., [tex]a_{8}=-8748[/tex]

Step-by-step explanation:

Given geometric sequence is 4,-12,36,...

Geometric sequence can be written as

[tex]a_{1},a_{2},a_{3},..,[/tex]

[tex]a_{1}=4=a[/tex]

[tex]a_{2}=-12=ar[/tex]

[tex]a_{3}=36=ar^2[/tex]

and so on.

common ratio is [tex]r=\frac{a_{2}}{a_{1}}[/tex]

[tex]r=\frac{-12}{4}[/tex]

[tex]r=-3[/tex]

[tex]r=\frac{a_{3}}{a_{2}}[/tex]

[tex]r=\frac{36}{-12}[/tex]

[tex]r=-3[/tex]

Therefore [tex]r=-3[/tex]

Geometric sequence of nth term is [tex]a_{n}=ar^{n-1}[/tex]

To find the 8th term:

[tex]a_{8}=ar^{8-1}[/tex]

[tex]a_{8}=ar^{7}[/tex]

here a=4 and r=-3

[tex]a_{8}=ar^{7}[/tex]

[tex]=4\times (-3)^7[/tex]

[tex]=4\times (-2187) [/tex]

[tex]=-8748[/tex]

[tex]a_{8}=-8748[/tex]

Therefore the 8th term of geometric sequence is -8748

Answer: it will need 40 cups of lemonade to break even

Step-by-step explanation:

Break even represents the point at which there is neither profit nor loss.

It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. Assuming that she made x cups of lemonade, the total cost of making x cups would be

30 + 0.5x

She sells each cup of the lemonade for $1.25 . Assuming that she sold x cups of lemonade, therefore, the total amount would be 1.25×x = 1.25x

To break even,

30 + 0.5x = 1.25x

1.25x - 0.5x = 30

0.75x = 30

x = 30/0.75

x = 40

Isn't this Anatomy and Physiology?

Answer:

The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.

Step-by-step explanation:

Let the amount of Strawberry juice in ounces be 'j'

Let the amount of water in ounce be 'w'

Given:

For each ounce of strawberry juice she uses three times as many ounces of water.

It means that amount of water in ounce is 3 times of amount of strawberry juice in ounce.

framing the equation we get;

[tex]w=3j[/tex]

Now we need how many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water.

We know that Total Strawberry infused water is equal to sum of amount of Strawberry juice in ounces and the amount of water in ounces

Framing in equation form we get;

[tex]j+w=64[/tex]

But we know [tex]w=3j[/tex]

hence,

[tex]j+3j= 64\\\\4j=64\\\\j=\frac{64}{4} = 16 \ ounces[/tex]

Hence amount of Strawberry juice = 16 ounces

Amount of water = [tex]3j = 3\times16 =48 \ ounces[/tex]

Hence The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.

This is a vertical line that goes through all points with an x-coordinate of -9.

To graph it, I can give you a couple of points this line goes through so you can draw it more easily.

Points that are on line: (-9,0) and (-9,1)

Answer:

Step-by-step explanation:

Ray hired sun and peter to help him move.

Let h represent the number of hours that each of them worked.

Let y represent Ray's total cost for hiring Sun and Peter for h hours.

Sun charged a $20 flat fee and $30 per hour. The total amount that Sun charges would be

20 + 30h

Peter charged $25 per hour. The total amount that Peter charges would be

25h

An expression for Ray's total cost if Sun and Peter each work h hours would be

y = 20 + 30h + 25h

y = 20 + 55h

Answer:

[20+(30+25)]h or (20+55)h

Step-by-step explanation:

20 will not be changed.

Total cost per hour is 55

add $20

Hope this helps

Answer:

[tex]5\frac{1}{4}[/tex] liters per hour.

Step-by-step explanation:

Consider the question: Ben drinks tea at an incredible rate. He drinks [tex]3\frac{1}{2}[/tex] liters of tea every [tex]\frac{2}{3}[/tex] of an hour. Ben drinks tea at a constant rate. How many liters of tea does he drink in one hour?

To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:

[tex]3\frac{1}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]

Convert mixed fraction into improper fraction:

[tex]\frac{7}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]

Convert division problem into multiplication problem by flipping the 2nd fraction:

[tex]\frac{7}{2}\text{ Liters}\times \frac{3}{2}\text{ hour}[/tex]

[tex]\frac{21}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]

[tex]5\frac{1}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]

Therefore, Ben drinks [tex]5\frac{1}{4}[/tex] liters per hour.

Answer:

He drinks 21/4, or 5 1/4, liters of tea in 1 hour

Step-by-step explanation:

The following question is missing: How much does he drink in one hour?

Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:

7/2 liters / x liters = 2/3 hour / 1 hour

x = (7/2)/(2/3) = 7/2 * 3/2

x = 21/4 = 5 1/4 liters

Answer:

Every point in the line would get reflected about the x axis and we would get a new line.

Step-by-step explanation:

When you reflect a point about the x-axis , the x-coordinate of the image remains the same but the y - coordinate changes to its negative value.

Now a line is a collection of points and we have to find out what happens when we reflect a line about the x-axis.

Reflecting a line about the line is same as keeping a mirror along the x-axis and the image we see in the mirror is the same as the image we obtain in the mirror.

So every point in the line would get reflected about the x axis and we would get a new line.

Final answer:

Reflecting a line across the x-axis inverts the y-coordinates of all points on the line, while the x-coordinates remain unchanged; the reflected line appears flipped over the x-axis, preserving distance but potentially changing orientation.

Explanation:

When a line is reflected across the x-axis, each point on the original line is flipped vertically to a new position on the opposite side of the x-axis, maintaining the same distance from the x-axis. Essentially, every point's y-coordinate is multiplied by -1, causing the line to appear as a mirror image of itself with respect to the x-axis. This transformation preserves the shape and size of the original line but changes its orientation relative to the x-axis.

Answer: 12 = r

Step-by-step explanation: When we have this kind of a setup, we want to put our variables together on one side of the equation and our numbers together on the other side of the equation.

First, let's put our variables on the right side by subtracting 3r from both sides of the equation. That gives us 5 = 2r - 19.

Now we can move our numbers to the left by adding 19 to both sides of the equation and we get 24 = 2r.

Divide both sides by 2 and 12 = r

Note:

Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper or digitally. It will really pay off for you down the line.

Answer:

The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].

Step-by-step explanation:

Let 's' represents the number of guest small tier can serve.

Let 'm' represents the number of guest medium tier can serve.

Now Given:

For First cake:

Number of small tiers = 3

Number of medium tier = 1

Total serving guest = 100

Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.

Framing in equation form we get;

[tex]3s+m=100[/tex]

For Second cake:

Number of small tiers = 3

Number of medium tier = 2

Total serving guest = 140

Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.

Framing in equation form we get;

[tex]3s+2m=140[/tex]

Hence The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].

Answer:

99% confidence interval is:

(0.00278 < P1 - P2< 0.15921)

Step-by-step explanation:

For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:

[tex][(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }[/tex]

             Where  [tex]p_{1}[/tex] : proportion sample of individuals who worked      

                                                     at more than one job in the city one

                           [tex]n_{1}[/tex]: Number of respondents in the city one

                           [tex]p_{1}[/tex] : proportion sample of individuals who worked      

                                                     at more than one job in the city two

                           [tex]n_{1}[/tex]: Number of respondents in the city two

Then

α = 0.01 and α/2 = 0.005

and [tex]z_{\alpha/2} = 2.575[/tex]

[tex]p_{1} = \frac{112}{384} = 0.2916[/tex]

[tex]p_{2} = \frac{91}{432} = 0.2106[/tex]

[tex]n_{1}= 384[/tex]  and [tex]n_{2}= 432[/tex]

The confidence interval is:

[tex][(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }[/tex]

(0.00278 < P1 - P2< 0.15921)

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].

where k is from 1 to 10.

By the given expression sequence will be [tex]\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......[/tex]

In this sequence first term "a" = [tex]\frac{1}{2}[/tex]

and common ratio in each successive term to the previous term is 'r' = [tex]\frac{\frac{(-1)}{4}}{\frac{1}{2} }[/tex]

r = [tex]-\frac{1}{2}[/tex]

Since the sequence is infinite and the formula to calculate the sum is represented by

[tex]S=\frac{a}{1-r}[/tex] [Here r is less than 1]

[tex]S=\frac{\frac{1}{2} }{1+\frac{1}{2}}[/tex]

[tex]S=\frac{\frac{1}{2}}{\frac{3}{2} }[/tex]

S = [tex]\frac{1}{3}[/tex]

Now we are sure that the sum of infinite terms is [tex]\frac{1}{3}[/tex].

Therefore, sum of 10 terms will not exceed [tex]\frac{1}{3}[/tex]

Now sum of first two terms = [tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]

Now we are sure that sum of first 10 terms lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{3}[/tex]

Since [tex]\frac{1}{2}>\frac{1}{3}[/tex]

Therefore, Sum of first 10 terms will lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{2}[/tex].

Option D will be the answer.

Answer: interest at the end of 3 years is $495.72

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 3 years

P = $3,672

R = 4.5%

Therefore

I = (3672 × 4.5 × 3)/100

I = 49572/100

I = 495.72

Answer:

1/8

Step-by-step explanation:

P(B) = 1/2

Now we are considering that the three children are all boys. This means we are considering that the first is a boy, the second is a boy and the third too is a boy. This brings us to the situation BBB

That is a boy and a boy and another boy. In probability, the word and means we multiply the three.

Hence:

P(BBB) = P(B1) * P(B2) * P(B3) = 1/2 * 1/2 * 1/2 = 1/8 or 0.125

The probability of a three-child family having all boys, given that each birth is independently a boy with a probability of one half, is 1/8 or 0.125 (12.5%).

The subject of your question is based in

probability

, a key concept in mathematics. Specifically, you're asking about the

probability of a family having three boys

, with the probability of any birth resulting in a boy being given as one half. As the question indicates that all births are independent, we're dealing with independent events in probability. The probability of independent events is calculated by multiplying the probabilities of each individual event. In this case, the probability of having a boy is one half (or 0.5), and we have three independent events (the births of the three children). Therefore, the probability of all three children being boys is (1/2) * (1/2) * (1/2), which simplifies to 1/8 or 0.125. So, assuming that all births are equally likely to result in a boy or a girl, the probability of a three-child family having all boys is 0.125, or 12.5%.

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