A gumball machine has 420 red gumballs. If the red gumballs are 75% of the total number of gumballs, how many gumballs are in the gumball machine?

Answer:

(5, 3)

Step-by-step explanation:

The given coordinates define a right triangle with (9, 8) as the vertex where the right angle is located. Then the other two coordinates define a diameter of the circumcircle. Its midpoint is the center.

... center = ((1, 8) +(9, -2))/2 = (5, 3)

6. f(1)+g(2) = 4

8. g(4)-f(0) = 18

10. 2g(-4) = 22

Put the number where the variable is and do the arithmetic.

f(1) = 2·1 -5 = -3

g(2) = |-3·2-1| = |-7| = 7

f(1) + g(2) = -3 + 7 = 4

___

g(4) = |-3·4 -1| = |-13| = 13

f(0) = 2·0 -5 = -5

g(4) - f(0) = 13 -(-5) = 18

___

g(-4) = |-3·(-4)-1| = |11| = 11

2g(-4) = 2·11 = 22

Answer:

2y^14

Step-by-step explanation:

= (-1/2)^3 · (y^4)^3 · (-16) · y^2

= (-1/8)·(-16) · (y^(4·3) · y^2) . . . . . simplify some

= 2 · y^(12 +2) . . . . . simplify more

= 2y^14

Answer:

The attachment shows ΔBAC ~ ΔBDA

Step-by-step explanation:

You want segment AB to be part of two similar, but not congruent, triangles. One way to do that is to make AB the hypotenuse of one triangle and the leg of another.

It is convenient to construct these triangles using point M as the arbitrary midpoint of the hypotenuse of the larger triangle. (We don't know the coordinates of M—we just know it is on the perpendicular bisector of AB.) BC is a diameter of circle M, and AD is the altitude of ΔABC.

Answer: First prism has the greatest volume.

Step-by-step explanation:

Since we have given that

Volume of prism = Length × Breadth × Height

So, we need to find the greatest volume, for which we find volumes of all figures:

1) Volume of prism would be

[tex]5\times 7\times 5\\\\=175\ cm^3[/tex]

2) Volume of prism would be

[tex]10\times 3\times 4\\\\=120\ cm^3[/tex]

3) volume of prism would be

[tex]7\times 7\times 3\\\\=147\ cm^3[/tex]

4) Volume of prism would be

[tex]5\times 3\times 7\\\\=105\ cm^3[/tex]

Hence, first prism has the greatest volume.

The volume of the prism with the Greatest volume is 250cm³

The volume of a prism is calculated by multiplying the prism's base area by its height. Mathematically expressed as

V = Base Area×Height

, it represents the space enclosed within the prism.

Since the prism is a cuboid, then

V = l × w × h

Where h is the height , l is the length and w is the width.

V = 5 × 5 × 10

V = 250 cm³

The volume of the prism is 250cm³

All are rational.

Any number you can write exactly and completely, or any repeating decimal is a rational number. Any number that can only be written exactly using a symbol, such as π or √2, is an irrational number. Something like √6.25 is rational, because it can be written exactly as 2.5, without the symbol.

The idea of "rational" means the number can be expressed as the ratio of two integers. Any integer can be expressed as the ratio of itself and 1.

All of your numbers can be expressed as the ratio of integers:

... -0.45 = -45/100 . . . . any terminating decimal can be expressed as a ratio of integers by making use of the place value multipliers

... 5/12 . . . . is the ratio of integers

... 0 = 0/1

... 247 = 247/1

Answer:

x=-7+8ı ,-7-8ı

Step-by-step explanation:

Move all terms to one side

x²+14x+17+96=0

Simplify x²+14x+17+96 to x²+14x+113

x²+14x+113=0

Use the quadratic Formula

x= -14+16/2 ,  -14-16ı/2

Simplify Solutions

x=-7+8ı ,-7-8ı

[tex]\dfrac{21}{49}=\dfrac{21:7}{49:7}=\dfrac{3}{7}\\\\\dfrac{21}{49}=\dfrac{15}{h}\to\dfrac{3}{7}=\dfrac{15}{h}\qquad\text{cross multiply}\\\\3h=(7)(15)\\\\3h=105\qquad\text{divide both sides by 3}\\\\\boxed{h=35}\\\\Answer:\ 35\ hours[/tex]

Answer:

[tex]\dfrac{-x+5}{6x^2-x-12}[/tex]

Step-by-step explanation:

The denominators are the same. You can add the numerators without any extra work.

[tex]=\dfrac{(4x+5)-(5x)}{6x^2-x-12}=\dfrac{-x+5}{6x^2-x-12}[/tex]

The denominator factors as (2x-3)(3x+4), so there are no factors that will cancel with the numerator.

Answer:

See the attached

Step-by-step explanation:

A graph of almost any exponential function quickly goes off-scale. The attachment shows a short table of values.

Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.

1000 = 2³·5³ . . . . a perfect cube

4 = 2² . . . . a perfect square

120 = 2³·3·5 . . . . none of the above (not a square or a cube)

36 = 2²·3² . . . . a perfect square

100 = 2²·5² . . . . a perfect square

49 = 7² . . . . a perfect square

125 = 5³ . . . . a perfect cube

25 = 5² . . . . a perfect square

For this case, we have that by definition:

Let "x" be an angle of any vertex of a right triangle.

[tex]Sin (x) = \frac {Cathet \ opposite} {hypotenuse}[/tex]

So, if we want to find the sine of angle A:

[tex]Sin (A) = \frac {3} {5}[/tex]

Thus, the sine of angle "A" is[tex]\frac {3} {5}[/tex]

Answer:

[tex]\frac {3} {5}[/tex]

Option A

The notation f(x) means you have a function that has been given the name f, and it makes use of the variable x. The variable in the parentheses is called the "argument" of the function f.

(a) To find f(q), you put q everywhere x is in the function equation. This is called evaluating the function for an argument of "q". In the following, note that we have simply changed x to q. (It's really that simple.)

... f(q) = q² -2q +3

(b) As in the previous case, we replace x with (x+h) everywhere.

... f(x+h) = (x+h)² -2(x+h) +3

You can multiply it out, but there appears to be no need to do so for this part of the question.

(c) The intent here is that f(x+h) and f(x) will be replaced by their values and the whole thing simplified. This requires you  expand the expression you see in part (b), subtract f(x), collect terms, and divide the whole thing by h. You have to make use of what you know about multiplying binomials.

We can do it in parts:

... f(x+h) = (x+h)² -2(x+h) +3

... = (x² +2xh +h²) + (-2x -2h) +3

Separating the h terms, this looks like ...

... = (x² -2x +3) + (2xh -2h +h²)

Now, we can finish the numerator part of the expression by subtracting f(x):

... f(x+h) -f(x) = (x² -2x +3) +(2xh -2h +h²) -(x² -2x +3)

You can see that the stuff in the first parentheses matches that in the last parentheses, so when we subtract the latter from the former, we get zero. We are left with only the terms containing h.

... f(x+h) -f(x) = 2xh -2h +h²

To finish up this problem, we need to divide this numerator value by the denominator h.

... (f(x+h) -f(x))/h = (2xh -2h +h²)/h

... = (2xh)/h -(2h)/h +h²/h

... = 2x -2 +h . . . . . this is the value of the expression

... (f(x+h) -f(x))/h = 2x -2 +h

Answer:

[tex]\dfrac{2}{3x^5y}[/tex]

Step-by-step explanation:

A negative exponent in the numerator is the same as a positive exponent in the denominator, and vice versa.

... a^-b = 1/a^b . . . . . for any value of b, positive or negative

The exponent of a product is the sum of the exponents:

... (a^b)(a^c) = a^(b+c)

___

Applying these rules, you have

... = 2/(3x^4·x·y) = 2/(3x^(4+1)·y) = 2/(3x^5·y)

See attached.

When graphing equations presented in standard form, it is often convenient to convert them to intercept for. You do this by dividing by the constant on the right, and expressing the x- and y-coefficients as denominators:

... x/(x-intercept) + y/(y-intercept) = 1

Dividing your equation by 48, you get ...

... x/12 + y/(-8) = 1

That is, the intercepts of the line are (12, 0) and (0, -8). A line through these points will be the graph of the equation.

5.3

The mnemoic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

... tan(24°) = x/12

Then multiplying by 12 gives ...

... 12·tan(24°) = x = 5.34274 ≈ 5.3

Answer:

A. 49°

Step-by-step explanation:

∠O is the other base angle (along with ∠Q) of the isosceles triangle OPQ. Base angles of an isosceles triangle have the same measure.

Answer:

a_0 = -27

a_n = a_(n-1) * (-1/3)

Step-by-step explanation:

First evaluate given formula at n=0 and specify that as starting value

Then find how to get from n-1 to n by comparing two values. In this case the next value is formed by multiplying by -1/3.

Answer:

[tex]a_n = a_{n-1} \cdot (-\frac{1}{3})[/tex]

Step-by-step explanation:

The explicit formula for the geometric sequence is given by:

[tex]a_n = a_1 \cdot r^{n-1}[/tex]

where,

[tex]a_1[/tex] is the first term

r is the common ratio to the following terms.

As per the statement:

Given the explicit formula for geometric sequence:

[tex]a_n = 9 \cdot (\frac{-1}{3})^{n-1}[/tex]

On comparing with [1] we have;

[tex]a_1 = 9[/tex] and [tex]r = -\frac{1}{3}[/tex]

The recursive formula for geometric sequence is given by:

[tex]a_n = a_{n-1} \cdot r[/tex]

Substitute the given values we have;

[tex]a_n = a_{n-1} \cdot (-\frac{1}{3})[/tex]

Therefore, the recursive formula for the geometric sequence is, [tex]a_n = a_{n-1} \cdot (-\frac{1}{3})[/tex]

Answer:

r = -0.9997  

Step-by-step explanation:

A statistics calculator gives the value

r = -0.9997

You can see in the graph below that it represents an excellent negative correlation between x and y.

Every point appears to be exactly on the regression line .

It represents a linear positive correlation between x and y −0. 999.

Given

The table shows Britney's distance, in miles, from her destination after different time intervals in hours:

Time (hours) (x) 2 4 1 3 6 5 7

Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690

A number between +1 and −1 is calculated so as to represent the linear interdependence of two variables or sets of data.

Then,

The correlation coefficient for the data, and what does it represent is;

It represents no correlation between x and y.

Hence, it represents a linear positive correlation between x and y −0. 999.

To know more about the correlation coefficient click the link given below.

brainly.com/question/12400903

$450

Each year, the amount of interest earned is ...

... 4.5% × $5000 = $225

After 2 years, a total of ...

... $225 × 2 = $450

has been transferred.

_____

Comment on percentages

Of course, you know that 4.5% = 4.5/100 = 45/1000 = 0.045.

You can think of the % symbol as a fancy (shorthand) way to write /100. (Likewise, the ‰ symbol means /1000.)

Answer:

(3, 8)

Step-by-step explanation:

For x = 3,

. . . y = 2^x

. . . y = 2^3 = 2·2·2 = 8

This is represented by the ordered pair (x, y) = (3, 8).

Answer:

(3,8)

Step-by-step explanation:

Since the answer choices are given we can plug the "x" value and see if it returns the y-value given in the ordered pair (x,y) and so:

[tex]y=2^x[/tex]

Let's use the ordered pair (3,8) meaning that when x=3 y =8 and so:

[tex]y=2^3=2\times2\times2=8[/tex]

[tex]y=8[/tex]

This is correct and so this is a solution, since the solution is unique when x=3 y is always going to return an 8.

The reasoning is correct. The ratio of number of bulbs tested to defective bulbs is always 14 to 1.

We generally expect industrial processes to produce defects at about the same rate, meaning the proportion of defective product is generally considered to be a constant. Here, the proportion of defective bulbs is ...

... 1/14 = 2/28 = 6/84

so we expect it will be also 24/336. That is, the ratio of the number of bulbs tested to defective bulbs is expected to remain constant at about 14.

Answer:

A. The reasoning is correct. The ratio of number of bulbs tested to defective bulbs is always 14 to 1.

Step-by-step explanation:

1–4: The interior angle of an n-sided regular polygon is (n-2)/n times 180°. For n ∈ {5, 6, 11, 4}, this is {3/5, 4/6, 9/11, 2/4} · 180°, or {108°, 120°, 147.3°, 90°}

5–8: The exterior angle of an n-sided regular polygon is 360°/n. For n ∈ {5, 9, 7, 4}, this is 360°/{5, 9, 7, 4}, or {72°, 40°, 51.4°, 90°}

Answer:

5(a+4)

Step-by-step explanation:

expression is equivalent to 5a+20

To get the equivalent expression we need to factor the given expression

5a+ 20

5a can be written as 5 * a

20 can be written as 5*2*2

WE can see that common factor is 5 for both 5a and 20

So GCF is 5

Now we factor out GCF 5

WE put 5 outside and write all the left of factors inside the parenthesis

5a +20

5 (a+2*2)

5(a+4)

Answer:

5(a+4)

Step-by-step explanation:

Answer:

30 units ^2

Step-by-step explanation:

To find the area of the shaded region, we find find the area of the large triangle and subtract the area of the unshaded triangle.

A of large triangle = 1/2 b*h

height = (6+3) = 9

The base is found by using the pythagorean theorem c^2 = a^2 + b^2

We need to  find b^2  

c^2 -a^2 = b^2

taking the square root on each side

sqrt(c^2 -a^2) = sqrt(b^2)

                           the base = sqrt(c^2 -a^2)

                                            = sqrt( 15^2 - 9^2)

                                            = sqrt(225-81)

                                             = sqrt(144)

                                              =12

Now that we know the base and the height, we can find the area

A of large triangle = 1/2 b*h

                               = 1/2 * 12 * 9

                              = 6*9 = 54

Using the rule of similar triangles

9               6

----  =  ----------

12           base

We can use cross products to find the base of the smaller triangle

9* base = 12*6

9* base = 72

Divide by 9 on each side

base = 72/9 = 8

Now we can find the area of the smaller triangle

base = 8 and height = 6

A of smaller triangle = 1/2 b*h

                                   = 1/2 *8 * 6

                                   = 4*6 = 24

Area of the shaded region = Area large triangle - Area of small triangle

                                              = 54-24

                                                = 30

Answer:

23 inches

Step-by-step explanation:

If we add 5 inches to the shortest side, all sides will be the same length and the perimeter will be 69 inches. The longest sides have length that is 1/3 that, or ...

... (1/3)·(64 +5 in) = 23 in

_____

You can solve for x, but you obviously don't need to.

The perimeter is ...

... (4x -2) + 2(4x -2 +5) = 64

... 12x +4 = 64

... 12x = 60

... x = 5

... 4x -2 +5 = 4·5 +3 = 23 . . . . the length of the longest side in inches

Answer:

9/16

Step-by-step explanation:

Since the area of a square is s^2, then ther area of this square is (3/4)^2 is 9/16.

The speed of the boat in still water is 12 mph, and the speed of the current is 9 mph.

Let's denote the speed of the boat in still water as ( b ) and the speed of the current as ( c ).

Downstream Trip:

The speed of the boat relative to the water is ( b + c ), and the distance is 210 miles.

Therefore, the time taken downstream is:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{b + c} \][/tex]

Given that this trip took 10 hours, we have:

[tex]\[ 10 = \frac{210}{b + c} \][/tex]

Upstream Trip:

The speed of the boat relative to the water is ( b - c ), and the distance is again 210 miles.

Therefore, the time taken upstream is:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{b - c} \][/tex]

Given that this trip took 70 hours, we have:

[tex]\[ 70 = \frac{210}{b - c} \][/tex]

Now, we have a system of two equations with two variables:

[tex]\[ 10 = \frac{210}{b + c} \][/tex]

[tex]\[ 70 = \frac{210}{b - c} \][/tex]

Solving this system of equations will give us the values of ( b ) and ( c ), which represent the speed of the boat in still water and the speed of the current, respectively. Let's solve it:

From the first equation:

[tex]\[ b + c = \frac{210}{10} = 21 \][/tex]

From the second equation:

[tex]\[ b - c = \frac{210}{70} = 3 \][/tex]

Adding the two equations:

(b + c) + (b - c) = 21 + 3

2b = 24

b = 12

Substituting ( b = 12 ) into ( b + c = 21 ):

12 + c = 21

c = 21 - 12

c = 9

So, the speed of the boat in still water is 12 mph, and the speed of the current is 9 mph.

Answer:

77°

Step-by-step explanation:

Angles B and C are adjacent angles of a parallelogram, so are supplementary.

... ∠C = 180° -∠B = 180° -103° = 77°

The measure of ∠BCD in a parallelogram with ∠B given as 103° is also 103° because opposite angles in a parallelogram are equal.

The measure of ∠BCD in a parallelogram can be found by using the property that opposite angles in a parallelogram are equal.

To find the measure of angle BCD, we can use the fact that angles in a quadrilateral sum up to 360 degrees.

We know that angle B is 103 degrees.

Since quadrilateral ABCD has sides AB and DC parallel, as well as sides AD and BC parallel, it is a parallelogram.

Given that ∠B is 103°, the measure of ∠BCD is also 103° because it is the angle opposite ∠B.