Three-fourths of students in your classroom like chocolate chip cookie dough ice cream. One-half of these same students also like mint-flavored ice cream. What fraction of students in your classroom like both flavors?
ANSWER FOR 100 POINTS

[tex]x^{2} + 2x - 15 = 0[/tex] -> [tex](x+1)^{2} - 16 = 0[/tex]

-> [tex](x+1)^{2} = 16[/tex]
-> x+ 1 = 4 or -4
-> x = 3 or -5

Answer:

[tex]x=3, \quad x=-5[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+2x-15=0[/tex]

Step 1

Move the constant to the right side of the equation:

[tex]\implies x^2+2x-15+15=0+15[/tex]

[tex]\implies x^2+2x=15[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=15+\left(\dfrac{2}{2}\right)^2[/tex]

[tex]\implies x^2+2x+1=15+1[/tex]

[tex]\implies x^2+2x+1=16[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+1)^2=16[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+1)^2}=\sqrt{16}[/tex]

[tex]\implies x+1=\pm4[/tex]

Step 5

Subtract 1 from both sides:

[tex]\implies x+1-1=-1\pm4[/tex]

[tex]\implies x=-1\pm4[/tex]

Solutions

[tex]\implies x=-1+4=3[/tex]

[tex]\implies x=-1-4=-5[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=3, \quad x=-5[/tex]

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Answer:

f=4

Step-by-step explanation:

I think it's right but not 100% sure

There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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Question 1

[tex]2l+2w=48 \\ \\ 2l+20=48 \\ \\ 2l=28 \\ \\ l=14\text{ cm}[/tex]

Question 2

[tex]2l+7.2=48 \\ \\ 2l=40.8 \\ \\ l=20.4 \text{ cm}[/tex]

Question 3

[tex]2l+2w=48 \\ \\ l+w=24 \\ \\ w=24-l[/tex]

Answer:

(y+5)(y-3)

Step-by-step explanation:

..........

Answer:

y^2-3y+5y-15

y(y-3)+5(y-3)

(y-3) (y+5)

Answer:

22

Step-by-step explanation:

The x-coordinates are the same, so we can find the positive difference between the y-coordinates, which is 22.

the answer is D) 22.

Step-by-step explanation:

3 ................

.

........................

Answer:

3

Step-by-step explanation:

–4 + (–16) + 23

–4 – 16 + 23

–20 + 23

= 3

Using proportions, it is found that the scale of the rectangle is of 1:14.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division to find the unit rates.

One example of application of proportions is for scale problems, as the scale is given by the following equation:

Scale = Drawn distance : Actual distance.

For this problem, we have that:

Hence the scale is of:

6.1 : 85.4.

We can simplify dividing 85.4 by 6.1, hence:

85.4/6.1 = 14.

Hence the simplified scale is:

1:14.

This problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the scale of the drawing of the rectangle.

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Answer:

£32

Explanation:

so 1/5 = 0.2

to make 0.2 a percent just multiply by 100 so 0.2 • 100 = 20%

so the discount would be 20%, meaning the game holds 80% of its value since

100-20 = 80

so to make 80% a decimal, divide by 100 so 80/100 = 0.8

so then you just multiply: 40 • 0.8 = 32

so the game is £32

hope this helps :)

The price of the computer game on sale is  £32.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The normal price of a computer game is £40.

The price is reduced by 1/5 in a sale.

∴ The price of the computer game on discount can be obtained if we subtract the fraction of the discount times the normal price from the normal price which is,

= {(40 - (1/5)×40}.

= {40 - 8}.

= £32.

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a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, 1/65 is the probability it’s a two-headed coin

Definition of probability

(1) : the chance that a given event will occur. (2) : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

We know that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.

We calculate  the number of possible combinations:

C₁⁶⁵= 65!/1!(65-1)!

     = 65

Number of favorable combinations is 1.

Therefore, the probability is

P=1/65.

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From the division property, the required kansui is 5/32 tablespoon.

What is division?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

Given that a batch of mooncake contains 1/4 tablespoon of kansui.

Given batch of mooncake is 1 3/5 = 8/5

Therefore,

[tex]\frac{\frac{1}{4}}{\frac{8}{5}}\\=\frac{1}{4} \times \frac{5}{8}\\=\frac{5}{32}[/tex]

Hence, the required kansui is 5/32 tablespoon.

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Answer:

21

Step-by-step explanation:

You are 14 right now if you were 7 yo 7 years ago. Add 7 more years to 14 and you get 21

Answer:

i dunno

Step-by-step explanation:

hard man

Answers:

a)  2710 kg/m³

b)  5149 kg

====================================================

Work shown for part a)

density = mass/volume

density = (6775 kg)/(2.5 m³)

density = (6775/2.5) kg/m³

density = 2710 kg/m³

-----------------------------------

Work shown for part b)

density = mass/volume

mass = density * volume

mass = (2710 kg/m³) * (1.9 m³)

mass = (2710*1.9) kg

mass = 5149 kg

Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars

New sales goal is 1,524,600 dollars.

Step-by-step explanation:

Answer:

D. The last 26/8, 3-32, -Pi, -4 2/3

Step-by-step explanation:

26/8= 3.25

3-32=3.17

-Pi= -3.14

-4 2/3= -4.67

Answer: [tex]y= \frac{-12}{5}x -2[/tex]

Step-by-step explanation:

1) Move x to the right.

1/4y = -1/2 - 3/5x

2) Multiply both sides by 4 to make y by itself.

-1/2 * 4 = -2 (Multiply the top by 4 and you will get -4/2 = -2)

-3/5x * 4 = -12/5x (Multiply the top by 4 and you will get -12/5x)

y= -2 - 12/5x

3) Reorder the terms so that x goes first.

y= -12/5x -2

Answer: y=-12/5(x-2)

Step-by-step explanation:

Move x to the right.

1/4y = -1/2 - 3/5x

2) Multiply both sides by 4 to make y by itself.

-1/2 * 4 = -2 (Multiply the top by 4 and you will get -4/2 = -2)

-3/5x * 4 = -12/5x (Multiply the top by 4 and you will get -12/5x)

y= -2 - 12/5x

3) Reorder the terms so that x goes first.

y= -12/5x -2

Thee surface area of the water tower is 1664 square feet

It is important to note that the formula for determining the surface area of a cylinder is expressed as;

Surface area = 2πr² + 2πrh

Where;

Also, note that the formula for diameter is expressed as;

Diameter = 2r

Substitute the value of diameter

30 = 2r

r = 15 feet

Now, substitute the values into the formula

Surface area = 2(3.14)(15)² + 2(3.14)(40)

expand the bracket

Surface area = 1413 + 251. 2

Add the values

Surface area = 1664. 2

Surface area = 1664 square feet

Hence, the value is 1664 square feet

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Answer:

x = 70

Step-by-step explanation:

(2x - 5) and 45 are same- side interior angles and sum to 180° , that is

2x - 5 + 45 = 180

2x + 40 = 180 ( subtract 40 from both sides )

2x = 140 ( divide both sides by 2 )

x = 70

Description of a Function : Consider two nonempty sets, X and Y. A relation that links exactly one element from X to Y is known as a function from X into Y.

f(x) = 5x-2 ?

Solution:

f(x) = 5x-2

5x-2 = 0

 5x = 2

    x = 0.4

f(0.4) = 5(0.4)-2

          = 0

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The midpoint of the given coordinates of points (0,-10) and (-6,-8) is  ( -3,-9 )

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point 1( 0,-10 )

Point 2( -6,-8 )

Midpoint = ?

To determine the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 0 + (-6) )/2, ( (-10) + (-8) )/2 )

M = ( ( 0 - 6) )/2, ( -10 - 8 )/2 )

M = ( ( -6 )/2, (-18 )/2 )

Midpoint M = ( -3,-9 )

Therefore, the midpoint of the coordinates is ( -3,-9 ).

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The maximum height of the skateboarder is 40.25 feet after 0.875 seconds

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let h(t) represent the height of the skateboarder after t seconds.

h(t) = -16t² + 28t + 8

The maximum height is at h'(t) = 0

h'(t) = -32t + 28

-32t + 28 = 0

32t = 28

t = 0.875s

h(0.875) = -16(0.875)² + 28(0.875) + 8 = 40.25 feet

Maximum height is 40.25 feet

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If the sales tax in your city is 4.4% and an item costs $3 before tax the amount of tax you would  pay on that item is $0.132.

Sales tax is the tax amount that is charge on goods customers buys.

Using this formula to determine the sales tax

Sales tax = Sales tax percentage × Cost of item

Where:

Sales tax percentage = 4.4% or 0.044

Cost of item = $3

Let plug in the formula so as to find the sales tax

Sales tax = 0.044 × $3

Sales tax = $0.132

Therefore the sales tax amount is $0.132.

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The result of the expression (5x[tex]10^{-3}[/tex]) (7×[tex]10^{-2}[/tex])  in scientific notation is 35×[tex]10^{-5}[/tex].

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ [tex]10^{8}[/tex].

The expression in scientific notation is

(5x[tex]10^{-3}[/tex]) (7×[tex]10^{-2}[/tex]) = 5×7 × [tex]10^{-3-2}[/tex]

                           = 35 × [tex]10^{-5}[/tex]

Therefore, the result of the expression (5x[tex]10^{-3}[/tex]) (7×[tex]10^{-2}[/tex]) in scientific notation is 35×[tex]10^{-5}[/tex].

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The Slope of the line q equals 3.

Given the slope of line r is -

slope = perpendicular / base

Finding the equation of line using coordinates (2,3) and (-1,4)

putting the values in the equation,

y2 - y1 / x2 - x1

⇒ 4-3 / -1 -2

⇒ 1/-3

⇒ -1/3

Slope of the line r is -1/3

As line q is perpendicular to line r,

Using the property, 2 lines perpendicular to each other have slope = negative reciprocal of slope 1

the slope of line q becomes 3

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The likes and dislikes of the people is given the priority and the product is altered according to the taste of the consumers , in order to increase the sale of the product .

It refers to the method of sampling , where the data or information is collected from a certain specified group of people , is referred to as quota sampling .

The method is helpful for marketing the goods and services of the company .

The likes and dislikes of the people is given the priority and the product is altered according to the taste of the consumers , in order to increase the sale of the product .

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The most appropriate choice of percentage will be given by-

£47 after 24% decrease becomes £35.72

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Here,

Original Price = £47

Percentage decrease = 24 %

Decrease in Price = £([tex]\frac{24}{100} \times 47\\[/tex])

                              = £11.28

New Price = £(47 - 11.28)

                 = £35.72

So, £47 after 24% decrease becomes £35.72

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