A survey was conducted among 1000 people. Of these 595 are Democrats, 595 wear glasses and 550 like ice-cream; 395 of them are Democrats who wear glasses, 350 of them are Democrats who like ice-cream, 400 of them wear glasses and like ice-cream, 250 of them are Democrats who wear glasses and like ice-cream. How many of them are not Democrats, do not wear glasses, and do not like ice-cream? How many of them are Democrats, who do not wear glasses, and do not like ice-cream?

The simplified expressions are 2^-2 and 60^6

Expression (a)

We have:

2^3 * 2^-5

Apply the product law of indices

2^3 * 2^-5 = 2^(3 - 5)

Evaluate the difference

2^3 * 2^-5 = 2^-2

Expression (b)

We have:

(60^2)^3

Apply the power law of indices

(60^2)^3 = 60^(2 * 3)

Evaluate the product

(60^2)^3 = 60^6

Hence, the simplified expressions are 2^-2 and 60^6

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Answer:

20% gained

Step-by-step explanation:

25 - 20 = 5

5 / 25 * 100 = 20%

Step-by-step explanation:

the solution is in the photo I sent

The prediction of the author about the future of the earth's mantle is that it would affect the sea level rise.

This refers to the statement that contains a forecast about future events that is made.

Hence, we can see that from the complete text, there is the scientific explanation of the lead researcher about the future of the Earth's mantle and how this would affect sea levels as they would increase.

Yes, I support his guess because he made use of past events and current happenings to show the effects on the sea levels.

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Answer:

14.58 gallons

Step-by-step explanation:

The tank volume is 3360 in^3, which is the product of the base x length x height (14)(12)(29) = 3360 in^3.

We are given a conversion factor:  1 fluid oz = 1.8 in^3

We can write this as (1 fluid oz)/( 1.8 in^3).

Use this conversion factor to confert volume to fluid oz:

(3360 in^3)*((1 fluid oz)/( 1.8 in^3)) = 1867 fluid oz

There are 128 fluid oz/gallon.  Make this into a conversion factor:

(1 gallon/128 fluid oz)  [The conversion factor can be written with oz or gallon on the top - it makes no difference since the two values are equal to each other]

(1867 fluid oz)*((1 gallon/128 fluid oz) = 14.58 gallons

water  the tank will hold = 14.583 gallons

Given : A fish tank  has a volume = 3360 cubic Inches.

        The length of the tank is =14 inches

                             the width is  = 12 inches.

         The height of the tank is = 20 inches.

           If one fluid ounce is = 1.8 cubic inches

Volume of tank = 14 * 12 * 20  =  3360 cubic inches

1.8 cubic inches   =  one fluid ounce

3360 cubic inches   =  3360/1.8   fluid ounce

= 5600/3    fluid ounce

As we know,

                  1 gallons  = 128   fluid ounces

water  the tank will hold    =(  5600/3 ) / 128

                                           = 175 / 1 = 14.583 gallons

Therefore, water  the tank will hold  = 14.583 gallons

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The actual payment Eric made to the bank at 175.00 for 36 months is 6,300

Actual payment to bank = Monthly payment × Number of months

= 175.00 × 36

= 6,300

Therefore, the actual payment made to the bank is 6,300.

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Answer:

(-1,-4) is the vertex

x = -1 is the equation of symmetry;

Step-by-step explanation:

See attached image.

Answer:

(- 1, - 4 ) and x = - 1

Step-by-step explanation:

given a parabola in standard form

y = ax² + bx + c ( ax≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 2x - 3 ← is in standard form

with a = 1, b = 2 , then

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

substitute x = - 1 into the equation for corresponding y- coordinate

y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4

vertex = (- 1, - 4 )

this is an upward opening parabola ( a > 0 )

the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex ), then equation is

x = - 1

Answer:

x = 20, so the labeled angles are 80° and 100°.

Step-by-step explanation:

[tex]5x + 4x = 180[/tex]

[tex]9x = 180[/tex]

[tex]x = 20[/tex]

So the labeled angles measure 80° and 100°.

Answer:

x = 20,the labeled angles are 80 and 100 degrees

Step-by-step explanation:

if we multiply them by 20 we will get 80 and 100

Part 1

By the inscribed angle theorem, arc ZY measures 76 degrees.

Part 2

Since angles inscribed in the same arc are congruent, angle YXZ measures 38 degrees.

Part 3

Since diameters form semicircles and the arc of a semicircle measures 180 degrees, arc XYZ measures 180 degrees.

Part 4

Subtracting arc ZY from arc XYZ, we get 104 degrees.

Answer:

y = 0.75x + 17

Step-by-step explanation:

y - 20 = 0.75(x-4)

y - 20 = 0.75(x) + 0.75(-4)

y - 20 = 0.75x -3

y = 0.75x -3 + 20

y = 0.75x + 17

y - 20 = 0.75(x - 4)    |add 20 to both sides

we can simplified equation:

use the distributive property: a(b + c) = ab + ac

y = 0.75x - 0.75 · 4 + 20

y = 0.75x - 3 + 20

Step-by-step explanation:

since DE is parallel to the diameter RS, D and E are just a transformation of R and S, where R and S slid up the same distance on the circle arc.

therefore, RD = SE.

and therefore d is half of the supplementary angle to the angle DE (that means together the angle DE and the supplementary angle are 180°).

so,

d = (180 - 50)/2 = 130/2 = 65°

Answer:

Step-by-step explanation:

The graphs of the transformations in each case are as follows;

a) f(x) = 5 -2 = 3

b) f(x) = 5

c) f(x) = 5

d) f(x) = 5+3 = 8.

The shifts, reflections, rotations and dilation operations are facilitated by transformation operations. On this note, it therefore follows that the graph of the given function as given is a straight horizontal line which is parallel to the x-axis and consequently, the transformations are as given above.

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Answer:

7/8 =0.875

Step-by-step explanation:

7/8 =0.875

4/5 =0.8

3/4 =0.75

Answer:

3/4

Step-by-step explanation:

Because if you had a Fraction Strip. 7/8 is a small Rectangle and 3/4 is a bigger Rectangle than 7/8. Look here: https://toytheater.com/fraction-strips/

Answer:

maximum 4 Mimimum I'm 0 or maximum 10 minimum 0

The value of  y = -32 , x = -8 .

Direct Variation is when a variable is dependent on the other variable such that , on increasing one variable the other also increases.

It is given that

x and y are two variables

and they are in direct variation

y ∝ x

y = k x

where , k is the proportionality constant

From the given data , y = 76 when x = 19

76 = k * 19

k = 4

The value of x , when y = -32

-32 = 4 * x

x = -8

Therefore for y = -32 , x = -8 .

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Using the given information, the original estimate was 18 months

From the question, we are to determine how long the original estimate was

Let the original estimate the x

Then, from the given information, we ca write that

x = 16 + (12.5% × 16)

x = 16 + (0.125 × 16)

NOTE: 12.5%  = 12.5/100 = 0.125

∴ x = 16 + 2

x = 18

Hence, the original estimate was 18 months

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Answer:

p, because Triangle ABC is similar to triangle EDC

Step-by-step explanation:

Angles DCA and DCE are vertical, so they are congruent.

Angles ABC and CDE measure 70°, so they are congruent.

Triangles BCA and DCE are similar by AA Similarity.

By corresponding angle of similar triangles, angles CED and BAC are congruent.

m<BAC = p

m<CED = m<BAC = p

m<CED = p

Answer:

$9.92 (rounded off to nearest cent)

Step-by-step explanation:

Square of 7-inch radius pizza = [tex]7^{2}[/tex] = 49 inches

49 Inches = $6

Square of 9-inch radius pizza = [tex]9^{2}[/tex] = 81 inches

Given 49 Inches = $6

1 inch =$ [tex]$(\frac{6}{49} \\)[/tex]

I will leave it as a fraction as it is not the final answer, rounding it off will result in a loss of accuracy.

81 Inches = [tex]81* \frac{6}{49} \\[/tex]

= $9.92 (rounded off to nearest cent)

Answer:

D

Step-by-step explanation:

Looks like from the y-intercept of (0, 4), it goes to (1, 7). Therefore, it should be 3, or D.

(Just to make sure, you can plug it into the slope formula to get (7-4)/(1-0), which should give you 3!)

The expression of function g(x) is [tex](\frac x2 - 1)^2[/tex]

The function is given as:

[tex]f(x) = x^2[/tex]

When the function is shifted right by 1 unit, the rule is:

f'(x) = f(x - 1)

So, we have:

[tex]f(x) = (x - 1)^2[/tex]

When the function is compressed horizontally by a factor of 2, the rule is:

f'(x) = f(x/2)

So, we have:

[tex]g(x) = (\frac x2 - 1)^2[/tex]

Hence, the expression of function g(x) is [tex](\frac x2 - 1)^2[/tex]

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Answer:

26

Step-by-step explanation:

Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.

The sum of the two digit number is 8: x+y=8

When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36

Now we have two equations and two unknown parameters, so we have enough information to find those parameters.

Solve for x:

X=8-y

plug in x:

(10y + 8-y) - (10(8-y)+ y) = 36

simplify:

(9y + 8) - (80-9y) = 36

18y - 72 = 36

y = 108/18 = 6

so if y=6, then x=8-y=8-6=2

so our number is 26. 62 is 36 greater than 26.

The shapes from the cross section are square, parallelogram, trapezium, kite, triangle and rectangle.

It is important to note that the cross section of a cube is a square.

From the cross section visible from the figure, we have the shapes;

Thus, the shapes from the cross section are square, parallelogram, trapezium, kite, triangle and rectangle.

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22/7 was considered while choosing the square's side length, the area of just one side of the remaining paper which is a multiple of 7.

Since the largest circle that can be encircled by a square has a diameter "d" equal to its side length, we may use "d" to conveniently calculate both the square's area and the circle's area.

The largest possibly circle has been cut from a piece of paper.

Square’s area = [tex]d^2[/tex]

Circle’s area =ᴨ[tex]d^2/4[/tex]

Simplifying-

(divide both area by [tex]d^2[/tex]) we find their ratio is 1:(ᴨ/4) or 4/ᴨ (square: circle), and the inverse, ᴨ/4 circle: square.

Therefore diameter of circle =14 cm.

Hence area of circle=πr2.

If you use 22/7 as an approximation for ᴨ, the circle’s area 22/28 of the square’s, the square’s area is 28/22 of the circle’s , it follows that the area outside the circle is (28–22)/28 of the square’s area, which is (28–22)/28 x 14 x14,

or 6/28 x 14 x 14,

or 3/14 x 14 x 14,

or 42 square inches or-

(4-ᴨ)/4 x 14 x 14

22/7, It's a rather accurate estimate.

22/7 was considered while choosing the square's side length, which is a multiple of 7.

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Answer:

Step-by-step explanation:

you find the L.C.M

18 234 270 324

 13 13 15 18

3 1 15 18

 5 1 5 6

 6 1 1

 1 1 1 ans=18×13×3×5×6=21060

It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.

Let pi be pipe 1 and pi2 be pipe 2

pi = 1 / 1

pi2 = 1 / 2

together = 1/1 + 1/2 ;

3/2 time ; 2/3 hour.

It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.

Problem-solving is the act of defining a problem; figuring out the motive of the problem; identifying, prioritizing, and deciding on alternatives for a solution; and implementing an answer.

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