George has 1,702 oranges in his storeroom. He
has to pack them in 152 crates. If he packs an
equal number of oranges in each crate, how
many oranges should he pack in each crate, and
how many will remain?

To solve the equation 4x + 2 = 12, we subtract 2 from both sides and then divide by 4, finding that x = 2.5. The change of base formula mentioned is not needed for solving this equation.

The question asks to solve the equation 4x + 2 = 12 for x, but references the change of base formula which is not relevant to solving this linear equation. Instead, we will solve it through simple algebraic manipulation.

Therefore, the solution to the equation 4x + 2 = 12 is x = 2.5.

64 large boxes and 60 small boxes.

Here we must use the concept of multiples. A multiple of a number result of the multiplication of that number by an integer. For instance, 2, 4, 6, 8 are multiples of 2. The following chart shows our statement:

[tex]\begin{array}{cccccccccc}Number\,of\,boxes & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\Large & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72\\Small & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90\end{array}[/tex]

So we need to choose the number of small and large boxes such that the sum is 124 boxes of sunglasses and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:

64 large boxes and 60 small boxes because 64 + 60 = 124 and 64 > 60

Answer:

A merchant selling sunglasses can place 8 large boxes or 10 small boxes into a carton for shipping.

If a total of 124 boxes are shipped, then the large boxes in the cartons must be a multiple of 8 which means either 16,56,64, 72,104.

We will choose that multiple of 8, which when subtracted from 124, gives the number that is divisible by 10.

As the larger boxes are more in quantity, we will choose 64 and 104.

[tex]124-64=60[/tex]

[tex]64/8=8[/tex] cartons

[tex]60/10=6[/tex] cartons

Total cartons are =[tex]8+6=14[/tex]

Also, [tex]124-104=20[/tex]

[tex]104/8=13[/tex] cartons

[tex]20/10=2[/tex] cartons

So, total cartons shipped = [tex]13+2=15[/tex]

So, both can be answers. As any options are not given, you can solve it whatever way you like.

Range is all the y values included in the graph. Look at the image below for the y values:

As you can see the highest y value this graph reaches is 6 and the lowest is -5 therefore the range is...

-5 ≤ g(t) ≤ 6

Hope this helped!

~Just a girl in love with Shawn Mendes

Step-by-step explanation:

Answer:

Since we have the diameter, we need to divide it in half to get the radius of 1.75. You then square it to get 3.0625. Next, multiply this by the height (or length in this case) to get 36.75. you can either leave it in terms of pi or multiply 36.75 to get your final answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

"Rectangular" includes "square," and in fact treating the rectangle as a square is the fastest way to "solve" this problem.  The perimeter of the rectangular area is 160 ft; dividing that by 4 yields 40 ft.  "40 ft square" describes the rectangle maximum area:  (40 ft)^2 = 1600 ft^2.

Alternatively, let W and L represent the width and length of the rectangle.  Then:

P = perimeter = 2W + 2L = 160 ft, or W + L = 80 ft, or W = 80 ft - L.

A = area = L*W = L(80 ft - L) = 1600 ft^2.  Rewriting this as a proper quadratic:

80L - L^2 - 1600 = 0, or  L^2 - 80L + 1600.  Note that this last result factors into (L - 40)^2 = 0, so L = 40 ft.  Then W = 80 ft - 40 ft = 40 ft.

This confirms that the max area is 1600 ft^2 = (40 ft)^2.

Final answer:

To find Tina's dog's fenced area dimensions, use an algebraic model with area and perimeter equations to solve for the dimensions optimizing the given constraints.

Explanation:

To determine the dimensions of the rectangular area for Tina's dog:

Answer:

The vertex is (-2, 2).

Step-by-step explanation:

2x^2 + 8x + 10

Convert to vertex form:

= 2(x^2 + 4x) + 10

= 2 [ (x + 2)^2 - 4] + 10

= 2(x + 2)^2 - 8 + 10

= 2(x + 2)^2 + 2.

Compare this with a(x - b)^2 + c:

b = -2 and c = 2.

The vertex is at

Answer:

2

Step-by-step explanation:

Answer:

C). 0 degrees

Step-by-step explanation:

The given equation is:

-4 + 6 sinx = -4 + 4 sinx

adding 4 on both sides:

4 - 4 + 6 sinx = 4 - 4 + 4 sinx

6sinx = 4sinx

dividing by 2 on both sides, we get:

6sinx/2 = 4sinx/2

3 sinx = 2 sinx

subtracting 2 sinx from both sides we get:

sin x = 0

x = sin⁻¹ (0)

x = 0 degrees

Answer:

(6 + 2(6))/4 = M

Step-by-step explanation:

because Andrew has 6 sweets and Jim has twice the treats so that means you have to multiply 3 by 6 and then u get 18 divide it by 4 since their total equals 4 times their total.

Answer:

To answer your question the graph will go 6 units to the right because the absolute value bar means the "-6" will become +6 so therefore 6 units right.

the pictures show the y=|x| & the y=|x-6|

Answer:

shift 6 units up

Step-by-step explanation:

When you are moving the graph from the center, you only have to put a 0 to the X and in that way you can know where is it going to be located

So it will end up like this:

y = lx - 6l= l0 - 6l= 6

So since its the absolute value, and in this case you have to move the graph upwards to the (0,6)

Answer:

a. 6 + 2(x + 4) = (3 – x)

Step-by-step explanation: just took the test

Answer:

A

Step-by-step explanation:

f(x) = 2x^2 – 3x + 1 is a function (its graph is a parabola that opens up), and it is one-to-one (Answer A).  For each input, x, this function will return one output.

Answer:

24

Step-by-step explanation:

factorial(4) = 4*3*2*1

factorial(4) = 24

Answer:

the answer is b

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The geometric mean finds the typical value of a set of numbers through multiplication. To find the geometric mean of two numbers, you take the square root of the product of the two numbers.

So in this instance, multiply the two numbers together:

[tex]2*8=16[/tex]

And take the positive square root of the product:

[tex]\sqrt{16}=4[/tex]

The geometric mean is different than the commonly-used arithmetic mean, which finds the central value of a set of numbers by dividing the set's sum total by how many numbers are in the set.

Final answer:

The geometric mean of 8 and 2 is calculated as the square root of their product, which is 4.

Explanation:

To find the geometric mean of 8 and 2, we use the formula for geometric mean which is the square root of the product of the numbers. Therefore, the geometric mean of 8 and 2 is the square root of 8 multiplied by 2, which is √(8×2).

Let's calculate it step by step:

Hence, the geometric mean of 8 and 2 is 4.

Answer:

= 70.2 ± 3.761  bpm

Step-by-step explanation:

The question is on calculating the confidence interval for a population mean

The general expression is

CI = x ± z * δ/√n   where;

CI = confidence interval,

 x = mean of sample,

 δ = standard deviation,

  n= is sample size

   z = z* value from standard normal distribution according to   confidence level given.

Given that;

n= 30   x =70.2    δ=10.51          z* for 95% CI = 1.96

Then applying the expression

CI = x ± z * δ/√n

[tex]=\sqrt{n} = \sqrt{30} =5.477\\\\=\frac{10.51}{5.477} =1.919*1.96=3.761\\\\[/tex]

Cl = 70.2±3.761

= 70.2 ± 3.761  bpm

Answer:

(-b,c)

Step-by-step explanation:

The coordinates are going to be the same as (b,c), except it is on the other side of the y axis, making it negative on the x axis. B is the replacement for x in this case, so the first option is correct. Hope this helps :)

Answer:

The correct answer is first option

(-b, c)

Step-by-step explanation:

From the figure we can see that, a trapezium.

To find the coordinates of W

The coordinates (-a, 0) and (a, 0) are  same distance from the O.

Similarly the coordinate W and (b, c) are same distance from the point Therefore the coordinates of W is (-b, c)  

The correct answer is first option

Answer:

a: 5.25 b: -0.33

Step-by-step explanation:

a:

4x - 5 = 16

isolate the variable. this is done by putting only the variable on the left side and the numbers on the right side. when moving the 5 to the right side, it is counted as a -5 because of the minus in front. when moving it, be sure to change from - to + and vice versa.

4x = 16 + 5

4x = 21

x = 21/4

x = 5.25

b:

same process

35 + 3x - 11 = 23

move the 35 to the right, changing it to a -35

3x - 11 = 23 - 35

move the -11

3x = 23 - 35 + 11

3x = -12 + 11

3x = -1

x = -1/3

x = -0.33

Hope I could help! If you have any trouble, tell me in the comments.

Answer:

a. [tex]x=5.25[/tex]

b. [tex]x=-0.33[/tex]

Step-by-step explanation:

You need to solve for the variable "x" in each equation. Then:

a. You need to add 5 to both sides of the equation:

[tex]4x - 5 +(5)= 16+(5)\\\\4x= 21[/tex]

Now you need to divide both sides of the equation by 4, getting:

[tex]\frac{4x}{4}=\frac{21}{4}\\\\x=5.25[/tex]

b. You need to subtract 35 from both sides of the equation:

[tex]35 + 3x - 11-(35)= 23-(35)\\\\3x-11=-12[/tex]

Add 11 to both sides:

[tex]3x-11+(11)=-12+(11)\\\\3x=-1[/tex]

Now you need to divide both sides of the equation by 3, getting:

[tex]\frac{3x}{3}=\frac{-1}{3}\\\\x=-0.33[/tex]

Answer:

Step-by-step explanation:

The intersection is the point where two equations meet. It is calculated by substituting terms into the equations involved. For the given systems of equation, calculations are as follows:

2x - y = 6

y = 2x - 6

We substitute the equation above to the second equation.

5x + 10y = –10

5x + 10( 2x - 6 )= –10

Simplifying, 

5x + 20x - 60 = -10

25x = 50

x = 2

Therefore, the intersection has the value of x equal to 2.

Answer with Step-by-step explanation:

The point of intersection of the graphs of system of equation is the solution to the system of equations.

So, we need to find the solution of the system of equations:

2x – y = 6

5x + 10y = –10

Multiplying first equation by 10 and add it to second equation.

5x+10y+10(2x-y)= -10+60

5x+10y+20x-10y=50

25x=50

⇒ x=2

Hence, value of x where the graphs of the equations  

2x – y = 6

5x + 10y = –10 intersect is:

x=2

Answer:

The possible dimensions are  y, 5y + 2 and y + 7.

Step-by-step explanation:

V = 5y^3 + 37y^2 + 14 y

y is common  to all 3 terms so

V = y(5y^2 + 37y + 14)

V = y (5y  + 2)(y + 7)

The expressions for the possible dimensions of the rectangular prism.

[tex]V = 5y^3 + 37y^2 + 14 y[/tex]. The possible dimensions are y, 5y + 2, and y + 7.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,

then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

The given expressions for the possible dimensions of the rectangular prism.

[tex]V = 5y^3 + 37y^2 + 14 y[/tex]

y is common to all 3 terms

so,

[tex]V = y(5y^2 + 37y + 14)\\V = y (5y + 2)(y + 7)[/tex]

By the comparison of the volume

[tex]V = a\times b \times c \: \: unit^3[/tex]

Therefore, the dimensions are a = y, b = 5y + 2, c = y + 7.

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Answer:

Step-by-step explanation:

Replace tan^2(x) with sin^2 (x ) / cos^2(x)

2 sec(x) sin^3(x) = cos(x) * sin^2(x) / cos^2(x)    Cancel cos(x) with cos^2(x)

2 sec(x) sin^3(x) = sin^2(x) / cos(x)                     Multiply by cos(x) both sides

2 sec(x)*cos(x)*sin^3(x) = sin^2(x)                      Divide sin^2(x) both sides

Note sec(x) and   cos(x) will cancel when multiplied. giving you one

2 sin^3(x) / sin^2(x) = sin^2(x) / sin^2(x)             Do the division

2 sin(x) = 1                                                           Divide by 2

sin(x) = 1/2

x = sin-1(1/2)

x = 30 degrees or 150 degrees.

So the answers are pi/6 and 5/6 pi

Answer:

The correct answer option is quadratic, because the height increases and then decreases.

Step-by-step explanation:

We are given the following data in the table which represents the height of an object over  time:

Time (s)          Height (ft)

     0                      5

      1                     50

     2                     70

     3                     48

We know that in situation where the values increase and then decreases, a quadratic model is used.

From the values given in the table, we can see that the values of height first increased and then decreased with the increase in time.

Therefore, the model used is quadratic, because the height increases and then decreases.

Answer:

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the intercept form of the equation of a straight line

[tex]\frac{x}{a}[/tex] + [tex]\frac{y}{b}[/tex] = 1

where a is the x- intercept and b the y- intercept

here a = - 2 and b = 3, hence

[tex]\frac{x}{-2}[/tex] + [tex]\frac{y}{3}[/tex] = 1

Multiply through by - 6

3x - 2y = - 6 ← equation in standard form

Substitute x = 2 and y = 6 into the left side of the equation and if equal to the right side then (2, 6) lies on the line

left side = (3 × 2) - 2(6) = 6 - 12 = - 6

Hence line passes through (2, 6)

Answer:

c

Step-by-step explanation:

The Greatest Common Factor [GCF] means the LEAST DEGREE TERM possible, plus finding a common factor, in this case, between 9 and 13, which is 1, but writing it is unnecessary.

I am joyous to assist you anytime.

The greatest common factor of 13c and 9c³ is "c".

To find the greatest common factor (GCF) of 13c and 9c³, we need to determine the largest term that divides evenly into both expressions.

First, let's break down each expression into its prime factors:

13c = 13 x c

9c³ = 3²  x c³

Now, let's identify the common factors between the two expressions:

Common factors of 13c and 9c³: c

To find the GCF, we take the product of the common factors, considering the lowest exponent for each common factor:

GCF = c

Therefore, the greatest common factor of 13c and 9c³ is "c".

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Final answer:

The importance of graphs in representing solutions to systems of inequalities for purchasing decisions.

Explanation:

Katie's Situation:

Each small tub costs $3, and each large tub costs $4.

Katie needs to buy at least 7 tubs and has $24 in her wallet.

Graph Representation: The graph with the shaded region where the solution to the system of inequalities lies would show the combinations of small and large tubs Katie can buy within her budget.

Answer:

(A) Joel wants to find the quotient of a number and four, minus thirteen.

Step-by-step explanation:

The correct description that can be written as the expression [tex]\frac{n}{4}[/tex] - 13 is 'Joel wants to find the quotient of a number and four, minus thirteen'.

Mathematically, an expression is a combination of numbers, variables, operations, and functions that are combined according to specific rules to represent a mathematical computation or relationship. It can be thought of as a mathematical phrase or formula.

By combining numbers, variables, operators, and functions, mathematical expressions can represent a wide range of computations and relationships.

Expressions are fundamental in mathematics as they allow us to represent and manipulate mathematical concepts, solve equations, evaluate formulas, and analyze mathematical relationships. They are used in various areas of mathematics, including algebra, calculus, geometry, and more.

Hence, the expression [tex]\frac{n}{4}[/tex] - 13 can be written as 'Joel wants to find the quotient of a number and four, minus thirteen'.

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The Dilation is an enlargement

Answer:

b

Step-by-step explanation:

Answer

Given

the relative frequency tables in the figure below (Note: the tables are not in the same order as in the problem statement)

Find

which table is best suited to answer the question

A) the percentage of home viewers who prefer to watch horror movies

B) the percentage of people surveyed who prefer to watch comedy movies at home

C) the percentage of viewers with a preference for drama who watch at the theater

Solution

The figure shows the best choices for answering A, B, and C.

table 2 is best for A (it is normalized by viewing location)

table 3 is best for B (it is normalized over the whole sample)

table 1 is best for C (it is normalized by genre)

Answer:

1/5 for both of them is your answer.

Step-by-step explanation:

Lets see so 5 numbers on a spinner and you want a 3 and a 4, so their is only one 3 and one 4 on a spinner so your fraction would be for both of them 1/5.

Hope my answer has helped you!

Step-by-step explanation:

[tex]\text{The point-slope formula of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Answer:

x < -5 + 3b

Step-by-step explanation:

-x + 3b >5

-x > 5 - 3b ..... flip inequality when multiplying both sides by -1

x < -5 + 3b (Answer)

Answer:

x<-5/2 + 3b/2 ( the fractions are supposed to be 5 over 2  and 3b over 2 btw)

Step-by-step explanation:

pls mark brainiest.