56
There are 134 third-graders and 167 fourth-graders at the annual school and
family picnic. The number of students is 7 times the number of adults.
Each picnic table can seat 9 people. How many picnic tables will need to be
set up for the picnic?
Show your work.
total
301. Student
PRACTICE TEST 1
+63
64
i
n
63
third graders and

Answer:

The domain would be 0 to 4 seconds

Step-by-step explanation:

According to the given conditions a ball was lying on the ground but when it was hit by Vanessa it was in the air for 4 seconds. We have to find the domain.

We know that the domain is the input values. According to the given statement it would start at time 0 and end when it hit the ground at 4 seconds.

Therefore the domain would be 0 to 4 seconds.

[0,4] ....

Answer:

2 and 3

Step-by-step explanation:

Answer:

The solution to the set of inequalities is on the shaded regions.For example point (10,10)

Step-by-step explanation:

The equations are

[tex]y>\frac{1}{3} x+5\\\\\\\\y<\frac{1}{3} x-1[/tex]

plot the equations on a graph tool as shown below and visualize the solution on the shaded areas.

The system of inequalities y>1/3x+5 and y<1/3x-1 has no solution (parallel lines).

Suppose there is inequality given as: y ≥ f(x)

The region it covers is the region of value pairs (x,y) for which this inequality holds true.

We've to draw the region covered by it.

For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).

The system of inequalities are;

y > 1/3x + 5

The solution of inequality A is the shaded area below the dashed line

y = 1/3x + 5

The slope of line is m = 1/3

Similarly,

y < 1/3x - 1

The solution to inequality B is the shaded area below the dashed line

y = 1/3x - 1

The slope of line is m = 1/3

Thus, The system of inequalities y>1/3x+5 and y<1/3x-1 has no solution (parallel lines).

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Answer:

The ordered pair (3,1/2) is not a common point, the statement is false

The solution is the point (0.667, 6.333) (common point)

Step-by-step explanation:

we have

[tex]y=2x+5[/tex] -----> equation A

[tex]y=\frac{1}{2}x+6[/tex] ----> equation B

we know that

If a ordered pair is a common point between the two lines,

then

the ordered pair must satisfy both equations

step 1

Verify if the ordered pair (3,1/2) satisfy equation A

substitute the value of x and the value of y in the equation A and then compare the results

For x=3, y=1/2

[tex]\frac{1}{2}=2(3)+5[/tex]

[tex]\frac{1}{2}=11[/tex] ----> is not true

The ordered pair don't satisfy the equation A

therefore

The ordered pair is not a common points both lines

The statement is false

step 2

Find the common point between the two lines

[tex]y=2x+5[/tex] -----> equation A

[tex]y=\frac{1}{2}x+6[/tex] ----> equation B

Solve the system of equations by graphing

The intersection point both graphs is the solution of the system (common point)

using a graphing tool

The solution is the point (0.667, 6.333) (common point)

see the attached figure

Answer:

The Slope Formula ( x1, y1 ) And ( x2, y2 )

Answer:

you subtract the exponents and divide the bases

Answer:

B. 24

Step-by-step explanation:

Subtract numbers from left to right.

[tex]\displaystyle 25.73-2.19=23.54[/tex]

Round to the nearest tenths.

[tex]\displaystyle 23.54=24[/tex]

24 is the correct answer.

Answer:

B. 24

Step-by-step explanation:

Estimation:

25.73 - 2.19 = 24

Answer:

A

Step-by-step explanation:

we have g(x) = 5x+3  

we know that 5x=f(x)

so g(x)=f(x)+3  

thus g(x) is obtained by adding 3 units to f(x)  

that's means the graph of g is obtained by translating the parent function f by 3 units up

Answer:

Step-by-step explanation:

There are two functions f(x) = 5x and g(x) = 5x + 3

This parent function f(x) has been translated to form a new function g(x) = 5x + 3

These linear functions can be represented by two lines y = 5x and y' = 5x' + 3

So when we shift line y = 5x by 3 units up on the y-axis then a new graph of

y = 5x + 3 will be formed.

Therefore, Option A is the answer.

Answer:

(0,0),(0,15),(20,25),(40,0)

Step-by-step explanation:

we know that

The feasible region is a quadrilateral

Let

A,B,C and D the vertices of the feasible region

see the attached figure

Observing the graph we have that

The coordinates of point A are (0,0)

The coordinates of point B are (0,15)

The coordinates of point C are (20,25)

The coordinates of point D are (40,0)

therefore

The answer is

(0,0),(0,15),(20,25),(40,0)

Answer:

A

Step-by-step explanation:

(0,0),(0,15),(20,25),(40,0)

Answer:

2

Step-by-step explanation:

because 2*2*2*2is equal to 16

The real fourth roots of 16 are: 2 and -2.

The detailed answer explains how to find the real fourth roots of 16 step by step, providing a clear solution.

The question: Find all real fourth roots of 16.

Step-by-step explanation:

Answer:

20 inches squared

This is because the area of a triangle is height times base divided by 2.

So it is 10*4/2, so the answer is 20 inches squared.

The area of the right angle triangle is 20 square inches.

The area of a right angle triangle is given by the formula,

Area = 1/2 * base * height .

where the base and height are the legs of the given triangle.

It is given that the legs of a right triangle measure 10 inches and 4 inches.

Thus we have the base of the triangle as 4 inches and height of the triangle as 10 inches.

  Area = 1/2 * 4 * 10 square inches .

∴ Area =  20 square inches.

Therefore, the area of the right angle triangle is 20 square inches.

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Answer:

x = 50

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 2 given angles in the lower triangle and subtract from 180 to find the third angle

third angle = 180° - (65 + 65)° = 180° - 130° = 50°

x = third angle = 50 ( vertical angles )

A triangle has to have three angles and they have to add up to 180 degrees so,

65+65=130

180-130=50

X=50 degrees because it is equal to the third angle.

Answer:

Angle measurements of 35°, 35°, and 110°

Angle measurements of 40°, 60°, and 80°

Step-by-step explanation:

If you specify only the three angles, you can have an infinite number of similar triangles of different sizes.

A is wrong. There can be only one triangle in which all three side lengths are specified.

C is wrong. The angles do not add up to 180°.

The descriptions which can describe more than one triangle is:

a)

Side lengths 6 ft, 8 ft and 10 ft.

First we check whether it form a triangle or not:

6+8=14>10

8+10=18>6

and

6+10=16>8

Yes, these side lengths form a triangle.

With the help of this only one unique triangle is possible.

b)

angle measurements of 35°,35° and 110°

First we check the sum of the angles:

35°+35°+110°=180°

Hence, more than one triangle is possible.

c)

angle measurements of 30°,40° and 50°

First we check the sum of these angles:

30°+40°+50°=120°≠180°

Hence, these angles measure do not form a triangle.

d)

angle measurements of 40°,60° and 80°

First we check the sum of these angles:

40°+60°+80°=180°.

Hence, more than one triangle is possible.

e)

side length of 4 cm, 6 cm and 9 cm.

First we check whether it form a triangle or not:

4+6=10>9

6+9=15>4

and

4+9=13>6

Hence, a unique triangle will be formed.

Answer:

b. [tex]\frac{1}{y^3}[/tex]

Step-by-step explanation:

Here we are given  [tex]y^{-3}[/tex] and are asked to simplify it. We are going to apply the law of exponents which says that

[tex]a^{-n}=\frac{1}{a^n}[/tex]

Hence applying this rule in our problem we get, where a=y and n=3

[tex]y^{-3}=\frac{1}{y^3}[/tex]

Hence our C) Option is correct

Answer:

a) maximum height is 156.25 ft

b) 6 seconds

Step-by-step explanation:

a) The maximum height can be found by finding the y-coordinate of the vertex. The vertex is the highest point in a parabola opened downward.

I start with by finding the t-coordinate of the vertex.

The t-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex] where the expression [tex]-16t^2+92t+24[/tex] will need to be compared to [tex]at^2+bt+c[/tex].

We see that [tex]a=-16,b=92,c=24[/tex].

So the t-coordinate of the vertex is [tex]\frac{-b}{2a}=\frac{-92}{2(-16)}=\frac{-92}{-32}=\frac{23}{8}[/tex].

We can find the h, the height, that corresponds to this t by using the equation [tex]h=-16t^2+92t+24[/tex] where [tex]t=\frac{23}{8}[/tex].

So inserting 23/8 for [tex]t[/tex].

[tex]-16(23/8)^2+92(23/8)+24[/tex]

Plugging into calculator gives you 625/4.

So the maximum height is 625/4 or 156.25.

b) Let's find how long it takes the ball to hit the ground. If the ball is on the ground, then the distance between the ball and the ground is 0.  So we are looking to solve h(t)=0 for t.

So this is equation we are solving for t:

[tex]-16t^2+92t+24=0[/tex]

These numbers are big but since all the terms have a common factor we can make them slightly smaller.

That is, we are going to divide both sides by -4 and see

[tex]4t^2-23t-6=0[/tex]

It looks like it could be possible to factor.

a=4

b=-23

c=-6

We need to find two numbers that multiply to be ac and add up to be b.

a*c=4(-6)=-24

b=-23

So -24=-24*1 and -23=-24+1.

We are going to replace -23t with -24t+1t giving up something that should be factorable by grouping.

[tex]4t^2-23t-6=0[/tex]

[tex]4t^2-24t+1t-6=0[/tex]

Group the first 2 together and group the last two together:

[tex](4t^2-24t)+(1t-6)=0[/tex]

Factor what you can from each pair:

[tex]4t(t-6)+1(t-6)=0[/tex]

Now each term has a common factor of (t-6) so factor that out giving you:

[tex](t-6)(4t+1)=0[/tex]

Set both factors equal to 0 giving you

t-6=0              or               4t+1=0

  t=6               or               4t  =-1

  t=6               or                 t=-1/4

So it hit the ground in 6 seconds.

Final answer:

The maximum height of the ball is calculated to be at 2.875 seconds, and by inserting this time back into the height function, we get the max height. To determine when the ball hits the ground, we solve the quadratic function for when h(t) equals zero, finding that it occurs at approximately 5.4 seconds post launch.

Explanation:

To calculate the maximum height of the ball, we need to find the vertex of the quadratic function, which gives us the time when the maximum height is reached. The function is in the form h(t) = -16t^2 + 92t + 24. The time at which the maximum height occurs can be found using the formula -b/(2a), where a and b are coefficients from the quadratic function. Here, a = -16 and b = 92, so the time is t = -92/(2*(-16)) = 92/32 = 2.875 seconds. Inserting this back into the height function gives us the maximum height:

h(2.875) = -16(2.875)^2 + 92(2.875) + 24

Now, to find when the ball hits the ground, we need to find the positive root of the height function where h(t) = 0. The quadratic formula h(t) = -16t^2 + 92t + 24 is used to find the time values when the ball is at the ground level. Solving this equation, we get two possible times, and we're interested in the positive one since time cannot be negative.

Thus, we get that the ball reaches the ground at approximately 5.4 seconds.

Answer:

Step-by-step explanation:

You take the upaid balance of $110 and multiply it by 2%

which will give you $2.20. Then you add the two together and you get your answer of $112.20.

$110.00 x 2% = $2.20

$110.00

   +2.20

$112.20

The new balance on the charge account after applying a 2% finance charge to the unpaid balance of $110 is $112.20.

The student is asking about calculating the new balance on a charge account after a monthly finance charge is applied. To find this, we use the original balance and calculate the finance charge based on the given percentage. Since the unpaid balance is $110 and the monthly finance charge is 2%, we compute the finance charge as $110 × 0.02 = $2.20. Adding this to the unpaid balance gives us the new balance: $110 + $2.20 = $112.20.

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Answer:I think it is 5000x32

Step-by-step explanation:

10,000 divided by 2 is 5,000

64 divided by 2 is 32

5,000 can’t go down into 100 the same amount of times for 32 to get to 8

The simplified form of 10,000 x 64 are,

⇒ 100x⁸

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

To find simplified form of √10,000x⁶⁴

Since, We can simplify as;

⇒ √10,000x⁶⁴

⇒ √(100)² (x⁸)²

⇒ 100x⁸

Thus, The simplified form of 10,000 x 64 are,

⇒ 100x⁸

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Answer:

Question 6: 6.8

Question 7: 8295

Step-by-step explanation:

Question 6:

Let's say that each hamburger costs x amount of dollars, and each soda costs y amount of dollars. For the first statement, we purchase 7 hamburgers (so 7 times x) and 3 sodas (3 times y) to add up to 27.95. As an equation, this means that 7x+3y=27.95. Similarly, for the second statement, 5x+4y=23.40.

Putting these two side by side, we get:

7x+3y=27.95

5x+4y=23.40

Using Gauss-Jordan elimination, we can multiply the first equation by -4/3 and then add that to the second equation, resulting in

[tex]-13x/3 = 27.95*(-4/3)+23.40\\[/tex]

Simplifying, we get

[tex]-13x = 27.95*(-4)+23.4*3\\\\-13x = -41.6\\\\x=3.2[/tex]

Question 7:

Take the number of students as x and the number of teachers as y. There are 35 times as many students as there are teachers, so 35y=x. We know that the students and teachers added up equal 8544-12=8532 (as 12 seats are empty in the auditorium that can seat 8544, 8532 must be occupied), so x+y= 8532. Since 35y=x, 35y+y+8532, 36y=8532, and y= 237. Since the number of students is equal to x, and x=35y, 35*y=35*237=8295 students.

Answer:

120 degrees

Step-by-step explanation:

You can just eyeball that it is greater than 90 degreees so it must be 120 degrees.

Answer:

see explanation

Step-by-step explanation:

Given

4(px + 1) = 64 ( divide both sides by 4 )

px + 1 = 16 ( subtract 1 from both sides )

px = 15 ( divide both sides by p )

x = [tex]\frac{15}{p}[/tex]

When p = - 5, then

x = [tex]\frac{15}{-5}[/tex] = - 3

To simplify the expression sin² X - sinX - 2 / sinX - 2, we need to factor the numerator and denominator separately and then cancel out the common factor of sin(X) - 2. The equivalent expression is sin(X) + 1.

To simplify the given expression, we can factor the numerator and denominator separately and then cancel out common terms. The numerator can be factored as (sin(X) - 2) (sin(X) + 1), and the denominator can be factored as (sin(X) - 2). By cancelling out the common factor of (sin(X) - 2), we are left with (sin(X) + 1) as the equivalent expression.

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Answer:

Option (D)

Step-by-step explanation:

Mean=[tex]\frac{Sum of observations}{Number of observations}[/tex]

here, observations are

1×1=1

2×2=2

3×3=9

4×1=4

5×1=5

6×2=12

7×3=21

8×1=8

9×1=9

10×0=0

hence, sum of observations =1+4+9+4+5+12+21+8+9+0=73

Number of observations are=1+2+3+1+1+2+3+1+1+0=15

Mean=[tex]\frac{73}{15}[/tex]

Mean=4.8..

nearest to 5 .

Hence, option (D) is correct.

The number that is closest to the mean of the distribution is 5.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Sum of numbers = (1 x 1) + (2 x 2) + (3 x 3) + (4 x 1) + (5 x 1) + (6 x 2) + (7 x 3) + (8 x 1) + (9 x 1) = 73

Total numbers = 1+2+3+1+1+2+3+1+1+0=15

Mean = 73/15 = 4.8 = 5

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Answer:

so b=-9 while c=12.

Step-by-step explanation:

If you have x-intercepts 1 and -4, then that means f(1)=0 and f(-4)=0.

You are given [tex]f(x)=-3x^2+bx+c[/tex]

So you have the system of equations to solve:

[tex]f(1)=-3(1)^2+b(1)+c=0[/tex]

[tex]f(-4)=-3(-4)^2+b(-4)+c=0[/tex]

Evaluating the exponents:

[tex]-3(1)+b+c=0[/tex]

[tex]-3(16)-4b+c=0[/tex]

Doing a little bit of multiplying:

[tex]-3+b+c=0[/tex]

[tex]-48-4b+c=0[/tex]

Let's add 3 on both sides of equation 1 and 48 on both sides of equation 2:

[tex]b+c=3[/tex]

[tex]-4b+c=48[/tex]

Subtracting the equations will eliminate c.

Let's do that:

[tex]5b+0c=-45[/tex]

[tex]5b=-45[/tex]

Divide both sides by 5:

[tex]b=\frac{-45}{5}[/tex]

Simplify:

[tex]b=-9[/tex]

If b=-9 and b+c=3 then -9+c=3 implies c=9+3=12.

so b=-9 while c=12.

To find b and c for the parabola y=-3x^2+bx+c with x-intercepts 1 and -4, we express the equation in its factored form, then expand it. From the expansion, we see that b=-9 and c=-12.

To find the values of b and c in the equation y = -3x^2+bx+c, where the x-intercepts are given as 1 and -4, we use the following steps:

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Step-by-step explanation:

When moving left, subtract from the x-coordinate and when moving right, add in the x-coordinate. When moving down, subtract from the y-coordinate and when moving up, add in the y-coordinate.

1) Given point = (0, 0). 3 units right and 4 units down means (0+3, 0-4) = (3, -4).

2) Given point = (5, 2). 4 units left and 2 units down means (5-4, 2-2) = (1, 0).

3) Given point = (-6, -1). 8 units right and 5 units up means (-6+8, -1+5) = (2, 4).

4) In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. So taking R = (-6,6). 2 units right and 6 units down means (-6+2, 6-6) = (-4, 0).

5) In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. So taking R = (6,-6). 7 units left and 4 units up means (6-7, -6+4) = (-1, -2).

Answer:

C. 16

Step-by-step explanation:

The distance between two points on the number line is the absolute value of the difference of their coordinates.

If the coordinates of two points on the number line are a and b, then the distance between the two points is

d = |a - b|

The coordinates here are -9 and 7.

distance = |-9 - 7| = |-16| = 16

Answer:

$57.75

Step-by-step explanation:

If 11 books cost $42.35,

11b=42.35

b=42.35/11

b=3.85

15 books will cost 15b.

15b

= 15*3.85

= 57.75.

15 Books will cost $57.75.

Answer:

57.75

Step-by-step explanation:

First I found the unit rate by dividing 42.35 by 11, which is 3.85.

second i multiplied the unit rate by 15 and got 57.75

Answer:

B, irrational

Step-by-step explanation:

We know that π is irrational, since it can not be written as a division between  natural numbers (a sub class of Real numbers called N), it's value is 3,1415(a whole bunch of decimals after this)

If you remove the decimal part of π by subtracting the integer part of it, that is the number 3. the result will still being and irrational number

Since π= 3(the rational part) +0,1415... (the irrational part)

The resut of π-=3= 0,1415...

Answer:

B). Irrational

If you are doing this on khan academy this should work

Step-by-step explanation:

Hi! It will be a pleasure to help you finding the solution to this problem, so let's solve each part:

[tex]\boxed{A. \ 1.50h+4}[/tex]

From the problem, we know the following data of the problem:

Our goal is to find the the expression for the total cost for parking at the beach for h hours. So:

Step 1: Since we have a fixed price, this value will appear in our expression:

[tex]4[/tex]

Step 2: Since Laval paid $1.50 for each hour, this can be represented as the following expression:

[tex]1.50h[/tex]

Finally, we can write total cost (C) as the sum of these two expressions:

[tex]C=1.50h+4[/tex]

Finally, our correct option is A:

[tex]\boxed{1.50h+4}[/tex]

5 hours

Here we have to find how many hours Laval spent at the beach knowing that he paid a total amount of $11.50. From the previous part, we know that our expression is:

[tex]C=1.50h+4 \\ \\ For \ C=11.50 \\ \\ 11.50=1.50h+4 \\ \\ Subtracting \ 4 \ from \ both \ sides: \\ \\ 11.50-4=1.50h+4-4 \\ \\ 7.5=1.50h \\ \\ Dividing \ both \ sides \ by \ 1.50 \\ \\ h=\frac{7.5}{1.50}=5[/tex]

Finally, he spent 5 hours at the beach

Answer:

a = 3/2

Step-by-step explanation:

Multiply both sides by -3

Simplify

Divide both sides by -4

Take a look at the photo:

Answer:

placement plan

Step-by-step explanation:

<3

As the senior marketing rep, Jake needs to develop a marketing plan. This plan would outline the business's advertising and marketing efforts for the year, including goals, strategies, tactics, a market analysis, and a budget.

Jake, as the senior marketing rep for a new chain of upscale hotels, is tasked with creating a marketing plan. A marketing plan is a comprehensive document or blueprint that outlines a company's advertising and marketing efforts for the coming year.

It would detail the business's marketing goals, the strategies and tactics to achieve those goals, an analysis of the current market situation, and a budget for the marketing activities. For an upscale hotel chain, it might include strategies such as premium pricing, high-quality service, and targeted advertising.

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