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vfiekz [6]
3 years ago
11

Barbara uses 1 3/4 teaspoons of sugar to make a cup of hot chocolate. How many teaspoons of sugar should be use to make 10 cups

of hot chocolate.
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
6 0
17.5 teaspoons of sugar
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Emma invested $41,000 in an account paying an interest rate of 2.6% compounded monthly. Assuming no deposits or withdrawals are
kvasek [131]

Answer: it will take 7 years for the value of the account to reach $49,300

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $41000

A = $49300

r = 2.6% = 2.6/100 = 0.026

n = 12 because it was compounded 12 times in a year.

Therefore,

49300 = 41000(1 + 0.026/12)^12 × t

49300/41000 = (1 + 0.0022)^12t

1.2024 = (1.0022)^12t

Taking log of both sides of the equation, it becomes

Log 1.2024 = 12t × log 1.0022

0.08 = 12 × 0.00095 = 0.0114t

t = 0.08/0.0114

t = 7 years

8 0
3 years ago
f(x) = 2<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="latex
loris [4]

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2  * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

7 0
2 years ago
Estimate the circumference of the circle with the given radius or diameter. Use 3.14 for ?. Round to the nearest unit. (Half. 24
Mice21 [21]

Answer:

The perimeter of a circle can be found by using the followinfg expression

P = 2*π*r

where

π = 3.14

r  = radius of the circle = half the diameter of the circle

In this case, if we are given the radius, we use

P = 2*π*r

If we are given the diameter, we use

P = 2*π*(D/2) = π*D

1) 27in

radius = 27in

P = 2*(3.14)*(27 in) = 169.56 in

diameter = 27 in

P = (3.14)*(27 in) = 84.78 in

2) 79 in

radius = 79 in

P = 2*(3.14)*(79 in) = 496.12 in

diameter = 79 in

P = (3.14)*(79 in) = 248.06 in

3) 1809 in

radius = 1809 in

P = 2*(3.14)*(1809 in) = 11360.52 in

diameter = 1809 in

P = (3.14)*(1809 in) = 5680.26 in

4) 152 in

radius = 152 in

P = 2*(3.14)*(152 in) = 954.56 in

diameter = 152 in

P = (3.14)*(152 in) = 477.28 in

5 0
3 years ago
Classify ∠2 and ∠6. Compare angle measures, and give the postulate or theorem that justifies it.
LenaWriter [7]

Answer:

Explanation

Step-by-step explanation:

Angles 2 and 6 are corresponding angles in a transversal meaning they have the same measure.

4 0
2 years ago
What is the answer to: -2x-y=-9
Nitella [24]
Y=9-2x, 9-2x=0, 2x=9, x=9/2, if you were asked to put it in standard form put down the first thing I said, if you were asked for solution then everything I said
3 0
3 years ago
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