Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.

The ratio between the fruit and vegetable is 1:3

Ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

We can simply say that a ratio is a fraction of one quantity over another quantity

In this case, we just have to figure the ratio between fruit and vegetables.

In the first column, we have fruit to vegetable as 2:6 = 1:3

In the second column, we have fruit missing. We can make that x.

Using the ratio between fruit and vegetable, when vegetable is 12, the fruit will be 12/3 = 4

The value of fruit in the second column will be 4.

In the third column, we have fruit as 6 and vegetable as y.

We can apply same ratio to get the vegetable which will be 6 * 3 = 18

In the third column, the vegetable is 18

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Answer:

A

Step-by-step explanation:

1. calculate discount

30/100 × 58 = 17.4

2. calculate sell price

58 - 17.4 = 40.6

3. calculate sales tax

7/100 × 40.6 = 2.842

4. calculate total price

sell price + sales tax = 40.6 + 2.842 = 43.442

The unit rate of the cost of the fluid per ounce is $0.11

How to calculate the cost of the fluid per ounce ?

Chee buys two pint bottle of juice

The two pints costs $3.52

The unit rate of the cost of the juice per fluid ounce can be calculated as follows

1 pint is equals to 16 fluid ounce

2 pints= 2 × 16

= 32

The cost per fluid ounce is

= 3.52/32

= 0.11

Hence the unit rate of the cost of the juice per fluid ounce is $0.11

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Angles ∠4 and ∠6 are the same side interior angles.

Interior angles are defined as the inner of two angles formed when two sides of a polygon intersect. Any of the four angles are formed when a third line intersects a pair of parallel lines.

If two angles are on opposite sides of a transversal, they are alternate. A transversal is a line that runs parallel to two horizontal lines. The alternate angles are alternate interior angles if they are located between the two parallel lines. The alternate angles are alternate exterior angles if they are located outside of the two parallel lines.

Angles ∠4 and ∠6 are known as alternate interior angles based on the information provided. As a result, you have the following options:

They are located on opposing sides of the transversal.

They are located between the two lines crossed by the transversal.

Therefore Angles ∠4 and ∠6 are the same side interior angles.

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Answer:

A See work below

B  7.07

C [tex]\sqrt{50}[/tex]

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]5^{2}[/tex] + [tex]5^{2}[/tex] = [tex]c^{2}[/tex]

25 + 25 = [tex]c^{2}[/tex]

50 = [tex]c^{2}[/tex]

[tex]\sqrt{50}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]\sqrt{50}[/tex]  = c  This is the exact answer.  [tex]\sqrt{50}[/tex] is an irrational number.  This means that it never terminates or repeats in the decimal form.

[tex]\sqrt{50}[/tex] ≈ 7.07 Rounded

Answer(s):

[tex]5\sqrt{2}[/tex] and [tex]7.07[/tex]

Step-by-step explanation:

substitute a=5 and b= 5 into Pythagorean Theorem:

[tex]a^2+b^2=c^2\\(5)^{2}+ (5)^{2} = c^2[/tex]

Simplify:

[tex]25+25=c^{2}[/tex]

[tex]50=c^{2}[/tex]

square root of c^2 and 50

[tex]\sqrt{50} =\sqrt{c^2} \\\\\sqrt{50} =c[/tex]

Use prime factorization to reduce [tex]\sqrt{50}[/tex] to [tex]5\sqrt{2}[/tex]

So here are the answers:

Radical form [tex]5\sqrt{2}[/tex]

Rounded to nearest hundredth: [tex]7.07[/tex]

Hope this answer helps :)

The equation of the blue line in the given graph is y = -x/2 + 2   .

In the question ,

a line graph is given,

we have to find the equation of the blue line .

to find the equation of line , we need at least two points ,

So , from the graph we can see that the two points from where the blue line passes the graph are (4,0)  and (0,2) .

the slope = (2-0)/(0-4)

m = 2/(-4)

m = -1/2

So , the equation of the line passing from the points (4,0) with slope -1/2 , is

(y - y₁) = m(x - x₁)

y - 0 = (-1/2)(x - 4)

y = -x/2 + 2

Therefore , The equation of the blue line in the given graph is y = -x/2 + 2   .

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Answer:

25.2 miles per gallon

Step-by-step explanation:

[tex]\frac{31.5}{1.25}[/tex]

Answer:

$2.54

Step-by-step explanation:

2 qaurt = 8 cups

20.32/8=$2.54 percup

Answer: 43/5

Step-by-step explanation: I multiplied the 5 and 8, which gave me 40. Then I added 3 and got 43/5.

Answer: 70 dollars in profit

Step-by-step explanation: 20 x 13.50 = 270 20 - 3 = 17 20 x 17 = 340 340 - 270 = 70

The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .

L'Hopital's Rule in calculus is used to evaluate weird limits that result in indeterminate forms that are 0/0, ∞/∞ .  These types of limits

(a) cannot be calculated by direct substitution of limit and/or

(b) can be evaluated but using a very long procedure .

that means if [tex]\lim_{x \to a} \frac{f(x)}{g(x)}[/tex] = 0/0  or ∞/∞ ,

then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

In the question ,

there are several indeterminant forms given which are  0.∞ ,  [tex]0^{0}[/tex] , [tex]1^{\infty}[/tex] , 0/0 ,  ∞ - ∞ , ∞/∞ ,  ∞⁰  .

By the definition of L'Hopital's Rule , the option that matches with the definition is 0/0 and ∞/∞ ,

So , the correct option is (d) 0/0 and (f) ∞/∞   .

Therefore , The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .

The given question is incomplete , the complete question is

Select EVERY indeterminate form to which L'Hopital's Rule can be directly applied to (there may be more than one).

(a) 0.∞

(b) [tex]0^{0}[/tex]

(c) [tex]1^{\infty}[/tex]

(d) 0/0

(e) ∞ - ∞

(f) ∞/∞

(g) ∞⁰

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A continuous function that has a domain of [-3, 4]  will include all the values as -3,-2,-1,-0,-1,-2,3,4

What do you mean by continuous function?

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous.

It is given that a continuous function has a domain of [-3,4]

According to the definition of closed interval,

[-3,4] will contain all the elements between them and including them.

Therefore, [-3,4] will contain elements as -3,-2,-1,-0,-1,-2,3,4

Hence, a continuous function that has a domain of [-3, 4]  will include all the values as -3,-2,-1,-0,-1,-2,3,4

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The area of the circular table is 1075.21 square inches.

Jada has a table. The table is circular in shape. She paints the table. The diameter of the circular table is 37 inches. We need to find out the area of the table. We will, first of all, find the radius of the circular table. Let the radius and the area of the table be represented by the variables "r" and "A", respectively.

The radius of a circle is equal to half its diameter.

r = 37/2

r = 18.5 inches

To find the area of the table, we will use the formula for the area of a circle.

A = πr²

A = π(18.5)²

A = 1075.21

Hence, the area of the circular table is 1075.21 square inches.

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The length of the line is 18 units.

If there are two point P( a, b) and Q (c, d) then the distance between P and Q is

d= √ ( c- a)² + ( d- b)²

Given points: ( -10 ,9 ) and ( 5, -1)

So, the distance between these two points

Using Distance formula

d= √ ( c- a)² + ( d- b)²

d = √(5 - (-10))² + (- 1- 9)²

d= √15² + (-10)²

d= √225+ 100

d= 18. 027 units

Hence, the length of the line is 18 units.

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Answer:

The solution to this problem is option (B) - 18 units

Step-by-step explanation:

I took the test and the test told me the answer is 18 so hence, choose option (B) as your answer.

Hope this helped:)

Answer:

The answer is eleven. 11

Answer:

good i will buy          

Step-by-step explanation:

The expression that is equivalent to xy^2/9 is [tex]x\sqrt[9]{y^{2} }[/tex] , the correct option is (d) .

an Algebraic Expression is defined as an expression that is written using the combination of variables and numbers joined by mathematical operators .

For Example : 2x+ 3y , 3y , 2xy are all algebraic expressions .

In the question ,

it is given that ,

the algebraic expression is xy^2/9 ,

we need  to find an equivalent expression to the given expression .

we know that the x^(1/n) is written as [tex]\sqrt[n]{x}[/tex] .

So , xy^2/9 = [tex]x.(y^{2})^{\frac{1}{9} }[/tex] =  [tex]x\sqrt[9]{y^{2} }[/tex]

Therefore , The expression that is equivalent to xy^2/9 is [tex]x\sqrt[9]{y^{2} }[/tex] , the correct option is (d) .

The given question is incomplete , the complete question is

Which expression is equivalent to xy^2/9 ?

(a) √(xy⁹)

(b) [tex]\sqrt[9]{xy^{2} }[/tex]

(c) x(√y⁹)

(d) [tex]x\sqrt[9]{y^{2} }[/tex]

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As per the given function, the local minimum is 1 and the local maximum is 9 and it can be written as (1, 9)

Local Minimum and maximum

The term Local maxima and minima are the maxima and minima of the function that arises in a particular interval.

Here the Local maxima would be the point in the particular interval for which the values of the function near that point are always less than the value of the function at that point.

Whereas the local minima would be defined as the point where the values of the function near that point are greater than the value of the function at that point.

Given,

Here we have the function f is increasing on the interval (1, 4) and decreasing on the interval (4, 9).

Here we need to determine and explain whether there is a local maximum or local minimum on the interval (1, 9).

According to the definition of the local minimum and local maximum,

While we looking into the given point,

We have identified that the resulting point is

=> (1, 4) => 1 (minimum)

=> (4, 9) => 9 (maximum)

Therefore, the minimum and maximum is (1, 9).

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

There is a 13.3% chance that a sample of 200 U.S students in grades 9 through 12 who attend public and private school will have 11% or fewer obese students if 13.7% of the population is obese this year.(Option D)

Given:

The 2013 national youth risk behavior survey (yrbs) reported that 13.7% of u.s. students in grades 9 through 12 who attend public and private school were obese.

consider the random sample:

200 US students

11% are obese.

Null hypothesis:

Null hypothesis = 13.7%

= 13.7/100

= 0.137

Alternative hypothesis = p < 0.137.

Therefore the null hypothesis = 0.137.

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The expression for the area of the given figure is: 18x

Given, figure:

we are asked to determine the area of the expression of the given figure.

Label the given figure and join the points G and C

Draw the required figure.

Observe that from the figure that, the shape consists of a square ABCG and rectangle FCDE.

Find the area of the given shape.

area of the given shape = ar(ABCG) + ar (FCDE)

= 3 × x × 6

= 18x

Therefore, the expression for the area of the given figure is 18x.

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The probability of a type I error in the case of the new blood test is 0.022.

Given;

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)

                         =0.022

Hence, the probability of a type I error is 0.022.

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ΔABC is not a right angled triangle.

What is right angled triangle?

A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

Main Body:

First let's find the length of the last side. We can do this by adding AB and BC together, then subtracting this amount from the perimeter of Triangle ABC, 22 cm.

ABC - (AB + BC) ⇒ 22 - (8 + 5)

                             =22 - 13 = 9 cm

The hypotenuse is always the longest side of a triangle, so we know that the side we figured out is the hypotenuse. Now we can use the Pythagorean Theorem to see whether the triangle is a right triangle.

Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse.

If a² + b² do equal c², then the triangle is a right triangle.

⇒8² + 5² = 9²

⇒64 + 25 = 81

⇒89 > 81

Therefore triangle is not a right triangle, but we know that it is obtuse since a and b together are longer than c.

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You could stand at 7 feet and still be completely in the shadow of the tree.

What is the property of a similar triangle?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion).

Given

You are standing such that a 63-foot tree is directly between you and the sun.

If you are standing 240 feet away from the tree and the tree casts a 270-foot shadow.

BC to be the height of the tree and DE to be the height of how tall you could be and still be completely in the shadow of the tree.

∠D = ∠B = 90 degrees

Therefore,

By the similar triangle property;

DE/BC = AD/AC

x/63 = (270-240)/270

x/63=30/270=0.11

x=63*0.11 = 7

Hence, you could stand at 7 feet and still be completely in the shadow of the tree.

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Z score of a 3rd grader who is 47 inches tall with mean of 52 inches and standard deviation of 2.5 inches is  2

Z- Score give an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , x = 47 inches

standard deviation = 2.5 inches

mean = 52 inches

z-score = x- μ / σ

putting all the values ,

z-score = 47 - 52 / 2.5

= -5 / 2.5

= -2

|Z| = 2

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The correct statements are

The expression is

3y(7 + 2x) + 9xy -10

The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication

The expression is

3y(7 + 2x) + 9xy -10

From the expression 3y is the first term is a factor and (7+2x) is also the first term is a factor

Therefore,

The 3y in the first term is a factor.

The (7 + 2x) in the first term is a factor.

Consider the second term

The 9 in the second terms is a coefficient

Last term 10 is a constant, but there is not suitable statement is given

Hence, the correct statements are

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Answer:

A 0

Step-by-step explanation: