Mr. Tieu spent $23 on apples, oranges, and bananas. He bought 10 more apples than oranges, and 6 fewer bananas than apples. How many of each kind of fruit did Mr. Tieu purchase if one apple costs 70 cents, one banana costs 50 cents, and oranges cost 80 cents each?
PLS HELP

Answer:

4 - 2*16 +

9 - 16 +

16

37

Step-by-step explanation:

Step-by-step explanation:

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

Answer:

6188

Step-by-step explanation:

Answer: 6188

Step-by-step explanation:

Answer:

(v - 6)(v + 4)

Step-by-step explanation:

v² - 2v - 24

v² + 4v - 6v - 24

v(v + 4) - 6(v + 4)

(v - 6)(v + 4)

The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

To prove that if lim an/bn = 0 and bn is convergent, then an is also convergent, we can use the limit comparison test. Since bn is convergent, we know that its terms approach 0. Therefore, we can choose a positive number ε such that 0 < ε < bn for all n. Then, we have:

lim (an/bn) = 0
=> for any ε > 0, there exists N such that for all n > N, |an/bn| < ε
=> for all n > N, an < εbn

Since ε is a positive constant and bn is convergent, we know that εbn is also convergent. Therefore, by the comparison test, an is convergent as well.

To show that the series ∑(ln n)/(n^3 ln n^1/2 e^n) converges, we can use the comparison test again. Note that:

ln n^1/2 = (1/2)ln n
ln n^3 = 3ln n

Therefore, we can rewrite the series as:

∑[(1/2)/(n^2 e^(ln n))] = (1/2)∑(1/(n^2 n^ln(e)))

Since n^ln(e) > 1 for all n, we have:

(1/2)∑(1/(n^2 n^ln(e))) < (1/2)∑(1/n^2)

The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

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The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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a) The pet shelter has 40% cats (20% black, 5% adopted), and 60% dogs (10% black, 10% adopted). 50% of non-black cats and dogs are adopted, b) 0.45, c) 0.19, d) 0.15, e) 0.375, f) 0.6.

a) The probability tree would look like this:

P(Cat) = 40%

P(Black Cat) = 20%

P(Adopted Black Cat) = 5%

P(Not Adopted Black Cat) = 95%

P(Not Black Cat) = 80%

P(Adopted Not Black Cat) = 50%

P(Not Adopted Not Black Cat) = 50%

P(Dog) = 60%

P(Black Dog) = 10%

P(Adopted Black Dog) = 10%

P(Not Adopted Black Dog) = 90%

P(Not Black Dog) = 90%

P(Adopted Not Black Dog) = 50%

P(Not Adopted Not Black Dog) = 50%

b) P(Not Black Dog & Adopted) = P(Not Black Dog) * P(Adopted | Not Black Dog) = 0.90 * 0.50 = 0.45

c) P(Black Cat & Not Adopted) = P(Black Cat) * P(Not Adopted | Black Cat) = 0.20 * 0.95 = 0.19

d) P(Adopted) = P(Adopted Black Cat) + P(Adopted Not Black Cat) + P(Adopted Black Dog) + P(Adopted Not Black Dog) = 0.05 + 0.50 + 0.10 + 0.50 = 0.15

e) P(Adopted | Cat) = P(Adopted & Cat) / P(Cat) = (0.05 + 0.50) / 0.40 = 0.375

f) P(Cat | Adopted) = P(Cat & Adopted) / P(Adopted) = (0.05 + 0.50) / 0.15 = 0.6.

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Complete question:

Pet shelters typically have special adoption events for black cats and dogs, since their adoption rate is lower. One specific pet shelter (which has only cats and dogs) has 40% cats and 60% dogs. Twenty percent of the cats are black, and 10% of the dogs are black. The adoption percentage for black cats is 5%, and for black dogs is 10%. Cats that are not black are equally likely to be adopted as not adopted, and this is the same for dogs that are not black. For (b)-(f), write the probability statement and then calculate your answer.

a) Draw the probability tree and label all events and probabilities in it.

b) What is the probability that a randomly chosen animal is not black, a dog, and is adopted?

c) What is the probability that a randomly chosen animal is black, a cat, and is not adopted?

d) What is the probability that a randomly chosen animal is adopted?

e) Suppose a randomly chosen animal is a cat, what is the probability that it is adopted?

f) Suppose a randomly chosen animal is adopted, what is the probability that it is a cat?

The lists that shows grade levels in order from the greatest fraction of students to the least fraction of students is of:

7th grade, 8th grade, 5th grade, 6th grade, 9th grade.

Here, we have,

A fraction is a numerical representation of the division of the two values x and y, as follows:

Fraction = x/y.

The terms are called as follows:

x is the numerator of the fraction.

y is the denominator of the fraction.

The decimal equivalent, which is used to order the fractions, of a fraction is obtained by the division of the numerator of the fraction by the denominator of the fraction.

Hence the equivalents of each fraction are given as follows:

5th grade: 33/50 = 0.66.

6th grade: 13/20 = 0.65.

7th grade: 18/25 = 0.72.

8th grade: 51/75 = 0.68.

9th grade: 3/5 = 0.6.

Hence the order from greatest to least is of:

7th, 8th, 5th, 6th, 9th.

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complete question:

The table shows the fraction of students from different grade levels who are in favor of adding new items to the lunch menu at their school.

Which list shows the grade levels in order from the greatest fraction of students to the least fraction of students?

Responses

7th grade, 8th grade, 9th grade, 6th grade, 5th grade

7th grade, 8th grade, 9th grade, 6th grade, 5th grade

9th grade, 6th grade, 7th grade, 5th grade, 8th grade

9th grade, 6th grade, 7th grade, 5th grade, 8th grade

8th grade, 5th grade, 7th grade, 6th grade, 9th grade

8th grade, 5th grade, 7th grade, 6th grade, 9th grade

7th grade, 8th grade, 5th grade, 6th grade, 9th grade

4/9

hope it helps...!!!

Answer:

\( \frac{4}{9} \)

Step-by-step explanation:

\( \frac{80 \div 10}{180 \div 10} = \frac{8 \div 2}{18 \div 2} = \frac{4}{9} \)

Hope this help you out =)

Based on the mentioned values and the provided informations, the quotient of 5 ÷ 1/4 is calculated to be  20 \(\frac{2}{3}\) . So, option D is correct.

To solve this problem, we need to divide 5 by 1/4. We can do this by multiplying 5 by the reciprocal of 1/4.

The reciprocal of 1/4 is 4/1, so we can rewrite the expression as 5 x 4/1, which simplifies to 20.

Therefore, the quotient of 5 ÷ 1/4 is 20 \(\frac{2}{3}\)

To elaborate further, 1/4 represents one part of the large rectangle, which has been divided into five equal parts. When we divide 5 by 1/4, we are essentially asking how many times 1/4 goes into 5.

Multiplying 5 by the reciprocal of 1/4, which is 4/1, is the same as dividing 5 by 1/4. This gives us a quotient of 20, which can also be expressed as a mixed number, 20 ²/₃.

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The complete question is :

large rectangle is divided into five equal parts. What is the quotient of 5 ÷ 1/4? The possible answers are A) 1/20, B) 5/4, C) 4/5, and D) 20 2/3.

Answer:

I'm not sure if i'm doing this right, but I got 75

Step-by-step explanation:

(5-2)5*5^1 =  75

The triangle which has one obtuse angle is known as an obtuse-angled triangle. So, the figure shows an obtuse angled triangle.

What is an obtuse triangle?

An obtuse triangle is a type of triangle that has one angle measuring more than 90 degrees. In other words, an obtuse triangle is a triangle that has one "obtuse" angle, where "obtuse" means "greater than 90 degrees."

The other two angles in an obtuse triangle are acute angles, meaning they measure less than 90 degrees each. The sum of the angles in any triangle is always equal to 180 degrees, so in an obtuse triangle, the sum of the two acute angles is always less than 90 degrees.

It is worth noting that an obtuse triangle cannot be a right triangle (a triangle with one 90-degree angle), and it also cannot be an equilateral triangle (a triangle with three equal sides and three equal angles measuring 60 degrees each).

If the figure in question has one angle measuring greater than 90 degrees, then it is an example of an obtuse-angled triangle. An obtuse-angled triangle is a type of triangle that has one obtuse angle (greater than 90 degrees) and two acute angles (less than 90 degrees). The sum of the angles in any triangle is always equal to 180 degrees, so in an obtuse-angled triangle, the sum of the two acute angles is always less than 90 degrees.

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Your complete question is :-Which kind of triangle it is ?

Answer:

5 hours, y= how much money it will cost, and x represents how many hours

Step-by-step explanation:

y= 15x+45

120= 15x+45

-45 -45

75= 15x

75/15×= 5 hours

Answer:

A is equivalent

Step-by-step explanation:

Answer:

A: 3b + 2a + 5c

Step-by-step explanation:

The statements about the relationship between the two triangles below that are true include the following:

B. Angle C is congruent to angle S

C. Angle D is congruent to angle T.

E. Triangle DCA is similar to triangle TSR.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the pairs of corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:

∠C ≅ ∠S

∠D ≅ ∠T

ΔDCA ≅ ΔTSR

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Complete Question:

Which statements about the relationship between the two triangles below are true? Check all that apply. Triangle ACD. Angle D is 60 degrees and angle A is 74.9 degrees. Triangle RST. Angle R is 74.9 degrees and angle S is 45.1 degrees.

- Angle C is congruent to angle T

- Angle C is congruent to angle S

- Angle D is congruent to angle T

- Triangle DCA is congruent to triangle TSR

- Triangle DCA is similar to triangle TSR

- Triangle CAD is similar to triangle TSR

- Triangle CAD is congruent to triangle TSR

π/32 is the area enclosed by the curve r= sin(8θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(8θ) =0

=> sin(8θ) =0

=> 8θ = 0,π

=> θ = 0, π/8

so a=0 , b= π/8

now  

   A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)    ------(i)

 so   \(r^2\) = (sin(8θ))^2

=>  \(sin^2\) ( 8θ )

ans we know that

cos(2α) = 1 -  2\(sin^2\) α

so   \(r^2\)  = (1- cos(16θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha\)

=> 1/4* \(\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha\)

here a=0 and b=π/8

after putting the value and solving the integral

A = π/32

so A is the area enclosed by r=sin(8θ) is π/32

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Answer:

7+3^2-2*5/4-1*2=

7+9-10/-2=

6/-2 or -3

3/4+1/8=

7/8 divided by 1/8=

7-2^2

3

-3<3

the second one is larger

Hope This Helps!!!

Answer:

$15 and $2,985

Step-by-step explanation:

Answer:

c is greater than or equal to -1.

Step-by-step explanation:

Subtract 3 from both sides, divide by 5.

I have attached the work to your problem below.

I hope this helps.

The appropriate p-value for the given test statistic and hypotheses is approximately 0.0253.

Tο determine the apprοpriate p-value fοr the given hypοthesis test, we need tο use the t-distributiοn and the t-statistic value οbtained.

Given:

Null hypοthesis (H0): μ = 130 (pοpulatiοn mean)

Alternative hypοthesis (HA): μ > 130 (pοpulatiοn mean)

T-statistic: t = 2.73

Degrees οf freedοm: df = 5

Tο calculate the p-value, we cοmpare the t-statistic tο the t-distributiοn.

Since the alternative hypοthesis is μ > 130, it is a οne-tailed test, and we are interested in the right tail οf the t-distributiοn.

Using a t-table οr a statistical sοftware, we can determine the p-value assοciated with the t-statistic and the degrees οf freedοm.

Fοr a t-statistic οf 2.73 with 5 degrees οf freedοm, the p-value is apprοximately 0.0257 (assuming a twο-tailed test).

Since we have a οne-tailed test, the apprοpriate p-value is half οf the twο-tailed p-value:

p-value = 0.0257 / 2 = 0.01285

Therefοre, the apprοpriate p-value fοr the given hypοthesis test is apprοximately 0.01285.

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The coordinates of the point on the unit circle corresponding to a central angle of 21 degrees are (0.93, 0.36), which is answer choice c.

The point on the unit circle corresponding to a central angle of 21 degrees can be found using the trigonometric functions sine and cosine.

In this case, the x-coordinate is equal to the cosine of the angle and the y-coordinate is equal to the sine of the angle.

Converting degrees to radians, we have:

x = cos(21) = 0.93

y = sin(21) = 0.36

A unit circle in mathematics is a circle with a radius of one, or one unit. The unit circle is frequently the circle with radius 1 that is located at the origin (0, 0) in the Cartesian coordinate system on the Euclidean plane, notably in trigonometry.

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The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

the answer is 2...........jpjpjp ion knowwwwwwwww

Step-by-step explanation:

The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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The fries costs $1.49

Addition in math is a process of combining two or more numbers.

Given that, Keith ordered a hamburger for $2.25, a medium raspberry ice tea for $1.25, and a small sundae for  $1.25. He also ordered French fries. All of these items totalled $6.24.

Let the price of fries be x,

Therefore,

$2.25 + $1.25 + $1.25 + x = $6.24

$4.75 + x = $6.24

x = $6.24 - $4.75

x = $1.49

Hence, the fries costs $1.49

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Answer:

9 x 10

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

\(\frac{9x+7}{2}\) - [ x - [ \(\frac{-2}{7}\) ]] = 36← distribute bracket by - 1

\(\frac{9x+7}{2}\) - x +\(\frac{x-2}{7}\) = 36

multiply through by 14 ( the LCM of 2 and 7 ) to clear the fractions

7(9x + 7) - 14x + 2(x - 2) = 504 ← distribute parenthesis on left side

63x + 49 - 14x +2x - 4 = 504 ← simplify left side

51x + 45 = 504 ( subtract 45 from both sides )

51x = 459 ( divide both sides by 51 )

x = 9

The exact numerical value of this expression depends on the precision of the decimal approximations of e.

To find the area A of the region bounded between the curve f(x) = 4 - e²x - 1 and the line g(x) = 2x + 1 over the interval [-2, 2], we need to calculate the definite integral of the absolute difference between the two functions over that interval.

Let's denote the absolute difference between f(x) and g(x) as h(x):

h(x) = |f(x) - g(x)| = |(4 - e²x - 1) - (2x + 1)| = |3 - e²x - 2x|

To find the area A, we integrate h(x) over the interval [-2, 2]:

A = ∫[-2,2] |3 - e²x - 2x| dx

Since the integrand is not continuous on the interval, we need to break it down into two separate integrals based on the intervals where the function changes sign. In this case, it happens at x = -1.

Therefore, the area A is given by:

A = ∫[-2,-1] (e²x + 2x - 3) dx + ∫[-1,2] (-e²x - 2x + 3) dx

Evaluating the integrals, we get:

A = [e²x + x²2 - 3x] [-2,-1] + [-e²x - x²2 + 3x] [-1,2]

Substituting the limits of integration, we have:

A = [(e²-1 + 1 - 3) - (e²-2 + 4 - 6)] + [(-e²2 - 4 + 6) - (-e²-1 - 1 + 3)]

Simplifying, we get:

A = [-e²-2 + e²-1 - 1] + [-e²2 + e²-1 + 3]

Therefore, the exact area A of the region bounded between the given curve and line over the interval [-2, 2] is:

A = -e²-2 + e²-1 - 1 - e²2 + e²-1 + 3

Note: The exact numerical value of this expression depends on the precision of the decimal approximations of e.

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The volume of a right rectangular prism is given by the formula **V = l × w × h**, where **V** is the volume, **l** is the length, **w** is the width, and **h** is the height²³. The units of volume are cubic units, which means that they are the same as the units of length raised to the third power. For example, if the length is measured in meters, then the volume is measured in cubic meters (m³).

In this case, the length is 8 meters, the width is 10 meters, and the height is 5 meters. Therefore, the volume is:

**V = 8 × 10 × 5**

**V = 400 m³**

The units of volume are cubic meters (m³) because the units of length are meters (m).

Answer:

Step-by-step explanation:

The units for the volume of a right rectangular prism are cubic units because it is a measure of three-dimensional space.

In this case, the length, width, and height of the prism are all given in meters. Therefore, the volume of the prism can be expressed in cubic meters (m³).

So the volume of the right rectangular prism with a length of 8 meters, a width of 10 meters, and a height of 5 meters is:

Volume = length x width x height = 8 m x 10 m x 5 m = 400 m³.

Therefore, the volume of the prism is 400 cubic meters (m³).