In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is
approximately normal with a mean of 528 and standard deviation of 117.

Answer:

w1= -1.4, w2= 3

Step-by-step explanation:

I will assume that "x" is a w since there is no x within the question

Solution

w

1

=−

5

7

,w

2

=3

Alternative Form

w

1

=−1.4,w

2

=3

Evaluate

5×∣4w−1∣=5w+40

Simplify

5∣4w−1∣=5w+40

Rewrite the expression

5∣4w−1∣−5w−40=0

Separate the equation into 2 possible cases

5(4w−1)−5w−40=0,4w−1≥0

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,4w−1≥0

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,w≥

4

1

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,w≥

4

1

w=−

5

7

,4w−1<0

Evaluate

w=3,w≥

4

1

w=−

5

7

,w<

4

1

Find the intersection

w=3

w=−

5

7

,w<

4

1

Find the intersection

w=3 w=− 57

Solution

w

1

=−

5

7

,w

2

=3

Alternative Form

w 1=−1.4,w 2

=3

The smallest domain element of the relation is 2

The domain of the function is the set of input values of the graph

The relation is given as

R = {(2, 3), (3, 3), (4, 4), (5, 7), (7, 9), (12, 11), (14, 13)}.

Remove the y values to determine the domain

So, we have

Rx = {2, 3, 4, 5, 7, 12, 14}

The smallest element in the above list is 2

So, we have

Smallest Rx = 2

Hence, the smallest domain element of the relation is 2

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Answer:

(1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7), (-4,8), (-5,9), & (-6,10)

Step-by-step explanation:

First, solve to alter the equation into a slope form instead of in standard form.

x+3y=12

Because x represents the slope, we need to transfer it to the other side of the equation. By subtracting it, it'll allow the equation to only have 3y on the left side of the equation and x will become negative x which will be added on to the 12 on the right side.

x+3y=12

-x       -x

+3y=-x+12

3y=-x+12

Next, you would divide the 3 underneath the y and the number 12 to allow the 3y to become y because y needs to be isolated in order for the slope intercept formula to work.

3y divided by 3 equals 3 and 12 divided by 3 is 4.

3y/3=-x+12/3

The final equation would look as follows:

y=-x+4

Hence, the y-intercept is 4 and the slope is -1.

You would then plot the origin coordinate of (0,4) and either go down one and right one or up one and left one; either way, you'll receive a negative slope looking like this: \

Some points on the graph would be: (1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7)

Hope this helps.

Noah and Lin each need 6 cups of sugar

Noah and Lin buy 12 cup bag of sugar and divide it evenly to make their recipe

If the entire sugar is consumed, the number of flour required by each person can be calculated by dividing 12 by 2

= 12/2

= 6

Hence each person will need 6 cups of flour for the recipe

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Answer:

8th grader

Step-by-step explanation:

They walked the the fastest since they walked 50 feet more than the 6th grader in 5 more seconds ( im sorry if you dont understand! i tried my best explaining it! hope this helps :) )

The simplification of difference of the given two rational expressions [tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}[/tex] is equal to 2(x-1)/ (x-2)(x+2).Restriction on the variables is given by x≠ -2,  x≠ 2.

As given in the question,

Given expression is [tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}[/tex]

Simplify the given two rational expressions by factorizing them,

[tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}\\\\= \frac{x}{(x-2)(x+2)}+\frac{1}{x+2}\\\\= \frac{x+x-2}{(x-2)(x+2)}\\\\= \frac{2x-2}{(x-2)(x+2)}\\\\= \frac{2(x-1)}{(x-2)(x+2)}[/tex]

Restriction on the variables is given by  x≠ -2,  x≠2.

Therefore, the  simplification of difference of the given two rational expressions [tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}[/tex] is equal to 2(x-1)/ (x-2)(x+2). Restriction on the variables is given by x≠ -2,  x≠ 2.

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The lengths of the diagonals are 8 and 24

Area of kite :

Area of kite is the space enclosed by a kite. A kite is a quadrilateral in which two pairs of adjacent sides are equal. The elements of a kite are its 4 angles, its 4 sides , and 2 diagonals.

In the given statement is :

Suppose the length of one diagonal of a kite is three times the length of the other diagonal. If the area of the kite is 96 square inches.

And, to find the lengths of the diagonals.

Now, Area of the kite is 96 sq. inches.

The length of one diagonal of a kite is x

and, other diagonal is three times to other diagonal

So, d2 = 3x

The area of a kite = 1/2 x (d1) x (d2)

96 = 1/2 × x × 3x

96 = [tex]\frac{3x^{2} }{2}[/tex]

192 = [tex]3x^{2}[/tex]

64 = x^2

x = [tex]\sqrt{64}[/tex]

x = 8

Therefore, The length of one diagonal is 8

and, other length of diagonal is 3x = 3x 8 = 24

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I'll do problem 6 to get you started

x = number of people training all 3 sports.

This is because all 3 sports are needed for the triathlon

There are 35 swimmers total. 9 of which are also cyclers (but not runners), and there are 13 swimmers who are also runners (but not cyclers)

That leaves 35-9-13-x people who are swimmers only. I'll leave this expression un-simplified so you can see where the numbers are coming from. Take note of where I'm placing this in the venn diagram below.

There are 32 cyclers. Of this group, 9 are swimmers (but not runners) and 11 are runners (but not swimmers). That leaves 32-9-11-x people who are cyclers only.

There are 38 runners. Of this group, 13 are swimmers (but not cyclers) and 11 are cyclers (but not swimmers). That leaves 38-13-11-x people who are runners only.

All of these values are honestly hard to keep track of. This is why a visual approach using a Venn Diagram is recommended. See the diagram below.

The idea is that every value in the diagram then adds up to the 58 total attendees. This helps form the equation needed to solve for x.

Such an equation is possible because each attendee participates in at least one of the sports mentioned. No values will be outside of all three circles at the same time.

(35-9-13-x)+(32-9-11-x)+(38-13-11-x)+(9)+(13)+(x)+(11)=58

-2x+72 = 58

-2x = 58-72

-2x = -14

x = -14/(-2)

x = 7

Answer:

45f - 42

Step-by-step explanation:

-5(-9f + 7) - 7

Expand -5(-9f +7) = -5(-9f) + (-5)(7) = +45f -35 or simply 45f - 35

5(-9f + 7) - 7  becomes 45f - 35 - 7 = 45f - 42

The value of s in the given figure is 28

The given parameters are:

m<TUW = m<VUW =62 degrees

TW = s + 56 and VW= 3s

From the figure, we have the following congruent equation

TW = VW

This means that

s + 56 = 3s

Evaluate the like terms

So, we have

2s = 56

Divide both sides of the equation by 2

So, we have:

s = 28

Hence, the value of s in the given figure is 28

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The situation can be represented by a geometric sequence with a(1) = 5000 and ratio or r = 3/4. At the start of the 10th day, the remaining helium volume is 375.42 cm³

Let a(n) be the volume of helium left in the balloon at the nth day.

Day 1: The balloon is filled with 5000 cm³ of helium. We can conclude the volume of  helium in day 1 is:

     a(1) = 5000.

Day 2: The volume of helium loses 1/4 from its initial volume. Hence,

     a(2) = (1 - 1/4) . a(1)

            = 3/4 . 5000 = 3/4 . 5000 = 3750

Day 3: The volume of helium loses 1/4 from its volume in day 2. Hence,

      a(3) = (1 - 1/4) . a(2)

             = 3/4 . 3750 = 2812.5

Continue the process, it will form a geometric sequence with a(1) = 5000 and ratio or r = 3/4.

To find the 10th term, use the nth term formula:

a(n) = a(1) . r^(n-1)

a(10) = 5000. (3/4)¹⁰⁻¹

        = 5000. (3/4)⁹ ≈ 375.42

Hence, at the start of the 10th day, the remaining helium volume is  375.42 cm³

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The sale price is $80.

Here the original price is $80.

there is no any valid data to find sale price so sale price should be$80

Profit and loss are expressions used to determine whether or not a sale is economic. In our diurnal lives, we use these expressions frequently. However, the difference between the two is appertained to as profit, If the selling price is advanced than the cost price. However, the difference is appertained to as the loss, If the selling price is lower than the cost price. The cost price of a product is the price at which it's bought. The selling price of a thing is the price at which it's vended. In this essay, we will study further about profit and loss.

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Answer:

5(2) + 5(-3)

Step-by-step explanation:

10 + -15 = -5

Answer:

The water cooler can hold approximately 23,6L

Answer: x=

7.5

Step-by-step explanation:

Answer:7.5

Step-by-step explanation:

move all unknowns to one side by either adding or subtracting from both sides

so, subtract 4x from both sides and you get 2x-10=5

now mode -10 to the other side by adding 10 to both sides. you get 2x=15

divide both sides by 2 to get x by itself

you get x=7.5

The number of pensioners in the sample is 40.

Given,

Visitors to a cinema are either adults, children, or pensioners.

The ratio of children to adult visitors is 1:2.

The ratio of adults to pensioners is 3:4.

A stratified sample of 85 is to be taken from the cinema visitors.

We need to find out how many pensioners should be in the sample.

Example:

Out of 10 pens, the ratio of the red and blue pens is a:b

The number of blue pens = [ b / (a + b) ] x 10

The number of red pens = [ a / (a + b) ] x 10

We have,

Total number of visitors = 85

children:adult  = 1:2

adults:pensioners = 3:4

Here,

Let,

The number of children be C.

The number of adults be A.

Number of Pensioners be P.

Now,

1C : 2A

    : 3A : 4P

3C : 6A : 8P

Now,

3C + 6A + 8P = 85

This means 8 is the ratio of pensioners.

= 8 / (3 + 6 + 8) x 85

= (8 / 17)x 85

= 8 x 5

= 40

Thus the number of pensioners in the sample is 40.

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An equation in slope intercept form the line which goes through the points (0,3) and (4,-5) is;

⇒ 2x + y = 3

Here,

The line passes through the points (0,3) and (4,-5).

We have to find an equation in slope intercept form the line which goes through the points (0,3) and (4,-5).

What is Equation of line?

The equation of line passes through the point (a, b) with slope m is;

y - b = m (x - a)

Now,

The line passes through the points (0,3) and (4,-5).

Hence, The slope is given as;

[tex]m = \frac{y_{2}-y_{1} }{x_{2}- x_{1} } = \frac{-5-3}{4-0} = -2[/tex]

Therefore, the equation of line is;

y - y₁ = m (x - x₁)

y - 3 = -2 (x - 0)

y - 3 = -2x

2x + y = 3

Hence, An equation in slope intercept form the line which goes through the points (0,3) and (4,-5) is;

⇒ 2x + y = 3

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Answer:

70,951 rounded to the nearest hundred is 71,000.

Step-by-step explanation:

Before the demolition, since the RCA dome was the home to the Indianapolis Colts,   and the attendance in 2001 and 2005 was 450,746, 457,373, the attendance will not continue to increase indefinitely.

Before it was demolished, the RCA Dome was home to the Indianapolis Colts. The attendance in 2001 was 450,746, and attendance in 2005,  the rate of change in attendance 2001 to 2005 was 1657, the attendance will not continue to increase indefinitely until it will continue to increase when the capacity of the stadium was reached, and the building new stadium will help them to accommodate more fans, since if the attendance is high.

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The given expression:

(3/8)*( 1 + √49)^2 - (4 - 1)^3

Can be simplified to -3.

So we have the equality:

(3/8)*( 1 + √49)^2 - (4 - 1)^3 = -3

Which means that the first option is the correct one.

Here we have the expression:

(3/8)*( 1 + √49)^2 - (4 - 1)^3

(I think is something like that)

And we want to simplify it, so first let's simplify the things inside the two parentheses.

The first one is:

1 + √49

We know that 7*7 = 49, then the square root of 49 is 7.

1 + √49 = 1 + 7 = 8

The other one is:

4 - 1 = 3

Replacing that in the expression we get:

(3/8)*( 1 + √49)^2 - (4 - 1)^3 = (3/8)*(8)^2 - (3)^3

Now we can solve the exponents:

8^2 = 8*8 = 64

3^3 = 3*3*3 = 27

Replacing that we get:

(3/8)*64 - 27 = 3*8 - 27 = 24 - 27 = -3

We conclude that the given expression:

(3/8)*( 1 + √49)^2 - (4 - 1)^3

Can be simplified to -3.

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Answer:

There are actually 20 occurrences of the digit "2" in the numbers {1,2,⋯,100}, though there are 19 numbers in the same range where the digit "2" appears.

Step-by-step explanation:

Hope this will be helpful for you.

Answer:C

Step-by-step explanation:

c

The equation that represents the situation is

11 (p - 382) = 506

where p represents the amount in dollars that Esmeralda earns each week.

Option C is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Weekly expenses = $382

Money saved after 11 weeks = $506

The equation that represents the given above situation:

Let p = amount earned per week.

We can write,

11p - 11 x 382 = 506

Taking 11 as common.

11 (p - 382) = 506

Now,

We can say that,

11 (p - 382) = 506, where p represents the amount in dollars that Esmeralda earns each week.

Thus,

The equation that represents the situation is

11 (p - 382) = 506

where p represents the amount in dollars that Esmeralda earns each week.

Option C is the correct answer.

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When you are given two sides but no measurement of the angle, such as a = 15 and b = 15, we can create an infinite number of triangles.

For instance:

How many different triangles can be made if we have side lengths of 15 and 15 and an angle value of 0 to 360 degrees?

Using a protractor, make one of the triangles with sides of 25 metres and 21 metres, an angle of 12 degrees, and a third side that can be changed to your preferred length. You've constructed a triangle.

Similar to this, we can create a completely different triangle by varying the third side's length and angle measurement.

It's crucial to remember that you select the side lengths and angle. This implies that you might choose differently. You may create an infinite number of distinct triangles by using the same angles.

As a result, we can make an infinite number of triangles using just one angle and one side length.

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Answer: False

Step-by-step explanation:

Because The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try!

Answer:

the 3 steps

Step-by-step explanation:

1. Rearrange the equation so "y" is on the left and everything else on the right.

2. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

3. Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

Answer: x=−8

Evaluate

2x−9=3x−1

Move the variable to the left side

2x−9−3x=−1

Subtract the terms

−x−9=−1

Move the constant to the right side

−x=−1+9

Add the terms

−x=8

Divide both sides

−1

−x

​

=

−1

8

​

Simplify

−1

−x =

−8

Solution

x=−8

Step-by-step explanation:

Hey!

2x-9=3x-1

Lets put the x on 1 side

2x 2x

- 2x -9= 3x-1

-9= x -1

-1 -1

-8 = x

X = -8 is your answer

Hope this helps!

Answer:

1

Step-by-step explanation:

replace x with -7

f(-7) = 5 - (-7)

f(-7) = 5 + 7

f(-7) = 12

The correct answer from each drop-down menu is as follows:

A quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. For the given quadratic function, the graph is a downward parabola because the coefficient of x² is negative.

Therefore, function p is a quadratic function.

When the length of the tomato patch is 8 feet, the area of the bell pepper patch is given by:

p(x) = -0.5x² + 6x

p(8) = -0.5(8)² + 6(8)

p(8) = -0.5(64) + 48

p(8) = -32 + 48

p(8) = 16 square feet.

From the graph, we can logically deduce that the maximum possible area occurred at x = 6 feet. Thus, maximum possible area is given by:

p(x) = -0.5x² + 6x

p(6) = -0.5(6)² + 6(6)

p(6) = -18 + 36

p(6) = 18 square feet.

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Answer:1.052

Step-by-step explanation: