A shopkeeper bought 26 apples from a fruit vendor for $37.70.How much did each apple cost?

Since the volume of the sphere V = 36π cm³is greater than that of the cone, V' = 21π cm³ the ice cream will overflow.

The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere

Now if the ice cream above is going to melt when it does, will it fit in the cone or will it overflow? Since the ice cream is a sphere, the ice cream will not overflow if the volume of the ice cream equals the volume of the cone. If is greater than the volume of the cone, it will overflow.

Now, since the ice cream is a sphere, its volume is given by V = 4πr³/3 where r = radius of sphere = 3 cm

So, substituting this into the equation, we have that

V = 4πr³/3

V = 4π(3 cm)³/3

V = 4π × 27 cm³/3  

= 4π × 9 cm³

= 36π cm³

Also, since the volume of the cone is given by V' = 1/3πr²h where r = radius of cone = 3 cm and h = height of cone = 7 cm

So, substituting the value of the variables into the equation, we have that

V' = 1/3πr²h

V' = 1/3π(3 cm)² × 7 cm

= 1/3π × 9 cm² × 7 cm

= 3π cm² × 7 cm

= 21π cm³

We see that V = 36π cm³ > V' = 21π cm³

Since the volume of the sphere is greater than that of the cone, the ice cream will overflow.

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A function [tex]P(t) = 170.(1.30)^t[/tex]  that gives the deer population P(t) on the reservation t years from now

We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.

We could see the deer population grow exponentially since each year there will be 30% more than last year.

Since we know that an exponential growth function is in form:

[tex]f(x) = a*(1+r)^x[/tex]

where a= initial value, r= growth rate in decimal form.

It is given that a= 170 and r= 30%.    

Let us convert our given growth rate in decimal form.

[tex]30 percent = \frac{30}{100} = 0.30[/tex]

Upon substituting our given values in exponential function form we will get,

    [tex]P(t) = 170.(1+0.30)^t[/tex]

⇒ [tex]P(t)= 170.(1.30)^t[/tex]

Therefore, the function [tex]P(t) = 170.(1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.

Complete Question:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

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Answer:

22

Step-by-step explanation:

2-4i and i=6

2-4(6)

=22

The correct definition for the lines drawn to circle with centre C are:

A circle is a spherical shape without boundaries or edges.

Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:

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Answer:

16/(8×2)=

16/8×2=

16-8/2=

8/2=

4

Step-by-step explanation:

first we subtract 8 from 16 and divide the result by 2.

If an Estate dealer sells houses and makes a commission of GHc3750 for the first house sold and receives GHc500 increase in commission for each additional house sold, for reaching a total commission of GHc6500, she must have sold 6.5 houses.

The number of houses the estate dealer sold to reach a total commission of GHc6500 can be determined using the mathematical operations of subtraction, division, and addition.

The total commission received = GHc6,500

The commission for the first house = GHc3,750

The commission for the remaining houses sold = GHc2,750 (GHc6,500 - GHc3,750)

The commission for additional sale of each house = GHc500

The number of additional houses sold = 5.5 (GHc2,750/GHc500)

The total number of houses sold = 6.5 (5.5 + 1 or the first house)

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The two numbers that are in both sequences and between 10 and 30 are 14 and 26.

An ordered set of numbers that adhere to a pattern or rule is referred to as a sequence in mathematics. Sequences can be defined in a variety of ways, such as a formula or a recursive definition, and they can be finite or infinite. Several branches of mathematics, including calculus, algebra, and number theory, employ sequences to explore and answer problems related to the behaviour of functions. For instance, sequences may be used to create fractals and other geometric patterns, predict the rise of populations or the spread of illnesses, and examine the distribution of prime numbers.

The given sequence is 4n - 5, and the nth term is 3n + 2.

For numbers between 10 and 30 in the sequence we have:

4n - 5 ≥ 10

4n ≥ 15

n ≥ 3.75

And,

4n - 5 ≤ 30

4n ≤ 35

n ≤ 8.75

Now, we calculate the sequence for n from 4 to 8:

When n = 4, 3n + 2 = 14

When n = 5, 3n + 2 = 17

When n = 6, 3n + 2 = 20

When n = 7, 3n + 2 = 23

When n = 8, 3n + 2 = 26

Hence, the two numbers that are in both sequences and between 10 and 30 are 14 and 26.

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Answer:

(a) To find the linear function, we need to determine the slope and y-intercept of the line that passes through the two given points: (50000, 7000) and (70000, 7800).

Slope = (change in y)/(change in x) = (7800 - 7000)/(70000 - 50000) = 800/20000 = 0.04

Y-intercept = 7000 - slope * 50000 = 5000

So the linear function that gives the account executive's compensation y for a given amount of monthly sales x is:

y = 0.04x + 5000

(b) To find the account executive's compensation for $75,000 in monthly sales, we can plug x = 75000 into the linear function we found in part (a):

y = 0.04(75000) + 5000 = 8000

So the account executive's compensation for $75,000 in monthly sales is $8,000.

If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).

The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27.

Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).

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77 is the value of Q in linear equation.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

P ∝ 1/Q

PQ = K

AT P= 11

Q = 28

11 * 28 = K

K = 308

AT P = 4

4Q = 308

Q = 77

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Answer:

Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?

Step-by-step explanation:

a) If a is 4/5 of b, then b is 5/4 of a.

To find what part of a is b, we divide b by a:

b/a = 5/4

This means that b is 5/4 times larger than a, or b is 125% of a.

To find what part of a is b, we subtract 1 from this fraction:

b/a - 1 = 5/4 - 1

b/a - 1 = 1/4

So, b is 1/4 of a, or b is 25% of a.

Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

Answer:

One way is to realize that since the total area is 1, the area below z = 1 is equal to 1 minus the area above z= 1 which we know from before is 0.1587. So the area below 1 is 1 - 0.1587 = 0.8413.

It will take 16 seconds to get to your class.

[tex]\bold{Distance}=\bold{Speed }\times \bold{Time}[/tex]

[tex]200m = 1.5m\div s \times t[/tex]

[tex]24=1.5\times t[/tex] (We want to get t by itself, so lets get rid of the [tex]\times1.5[/tex] by dividing both sides by 1.5)

[tex]t = 16 \ \text{seconds}[/tex]

Therefore, it will take 16 seconds to get to your class.

The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

Answer:

<1= 61

<2= 61

<3= 119

Step-by-step explanation:

The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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The number which, when subtracted from 80, results in -30 is equal to 110.

To solve this problem, we can use algebraic equations to represent the given information. Let x be the number that we want to find.

According to the problem, when we subtract x from 80, we get -30:

80 - x = -30

To solve for x, we can isolate it on one side of the equation by adding x to both sides, and then simplify:

80 - x + x = -30 + x

80 = -30 + x

Next, we can isolate x by subtracting -30 from both sides:

80 - (-30) = x

Simplifying the right-hand side:

80 + 30 = x

110 = x

Therefore, the number that was subtracted from 80 and gave -30 as the result is 110.

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The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².

Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.

The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.

In this figure,

The 5cm flap will be adjacent to the side x. Therefore,

Length of the side x= 5cm

Area of the shaded region= l×b

because the shaded region is a rectangle.

area= 9*x

       =9*5= 45 cm²

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The solution to the system of equations y=-7x-29 and y=-3x-9 using elimination method is x = 5 and y = -64.

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate y by subtracting the second equation from the first. This gives us:

y - y = -7x - 29 - (-3x - 9)

0 = -4x - 20

Simplifying this equation, we get:

x = 5

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:

y = -7x - 29

y = -7(5) - 29

y = -64

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Complete question is:

Solve the given System of equations by elimination method

y=-7x-29,  y=-3x-9

Sampling distribution of sample means with size 10, drawn randomly from a population with unknown mean and standard deviation, is approximately normal. It has a mean of 32 and a standard deviation of 6.32 (standard error of the mean). Option D is correct.

The sampling distribution of the mean of a large enough sample size follows a normal distribution, even if the underlying population is skewed.

The formula for the standard deviation of the sampling distribution of the mean is( σ / [tex](\sqrt(n))[/tex] ) ,

where sigma is the standard deviation of the population and n is the sample size.

Substituting the values, we get:

standard deviation of sampling distribution =[tex]20/(\sqrt(10))[/tex]= 6.32

Therefore, the sampling distribution of all possible samples of size 10 is approximately normal with a mean of 32 and a standard deviation of 6.32.

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The probability that fewer than 3 of them use their smartphones in meetings or classes is 0.0366.

The binomial probability distribution is a discrete probability law with two parameters: trial number (n) and success probability (p) (p). When there are two mutually exclusive outcomes of finite trials, the binomial distribution is utilised.

The probability that a specific 3 people all use their smartphones in meetings or class is 0.53³.

Probability that remaining 7 people do not use their phone is 0.47⁷

¹⁰C₃ = 10*9*8/(3*2*1) = 120.

Thus, the probability of exactly 3 people using their smartphones in meetings or in class is 10C3*0.533*0.477, or 0.0905.

So, adding up the 3 possibilities (that 0 of them, 1 of them, or 2 of them use their smartphones in meetings or class) we get

¹⁰C₀*0.530*0.4710 + ¹⁰C₁*0.531*0.479 + ¹⁰C₂*0.532*0.478 = 0.0366.

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Complete question:

Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

Answer:

9

Step-by-step explanation:

-5 + (-18) +32

-23 + 32

32 -23

Answer:

The other is 75/7.

Step-by-step explanation:

Let the other rational number be x, then:

(-7/15) * x =  -5

x = -5 * -15/7

  = 75/7

From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.

a. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:

x ≥ 0 (non-negative amount of loam soil)

y ≥ 0 (non-negative amount of peat soil)

x + y ≤ 120 (total amount of soil sold is at most 120 tons)

x ≤ 60 (maximum amount of loam soil available is 60 tons)

y ≤ 90 (maximum amount of peat soil available is 90 tons)

To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;

The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.

b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:

P(x, y) = 50x + 75y

To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.

The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:

P(0, 0) = 0

P(60, 0) = 3000

P(60, 60) = 9000

P(30, 90) = 6750

P(0, 90) = 6750

Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.

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The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.

According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.

Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.

Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.

Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

So the answer is 120.

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The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².

Quotient:

The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.

Based on the given conditions, Formulate:

6.208× 10⁹ /9.7×10⁴

Simply using exponent rule with same base:

[tex]a^n. a^m = a^(n+m)[/tex]

= 6.208 × 1/9.7

Now,

the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³

Now solving, we get:

6.208/9.7 × 10¹³

Converting fraction into decimal, we get:

  0.64× 10¹³

⇒ 6.4 × 10¹²

Therefore,

The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².

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The best point estimate for the average number of school books per semester for all students at the local college is 5.2.

The average number of school books per semester for all students at the local college is 5.2. A sample of 39 students was taken, i.e., n = 39. To find, The best point estimate for the average number of school books per semester for all students at the local college.

The best point estimate for the average number of school books per semester for all students at the local college is the sample mean which can be calculated.

Therefore, the best point estimate for the average number of school books per semester for all students at the local college is 5.2.

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