George mixes 1/4  cup of sugar with 1/8 cup of honey. Give the ratio of sugar to one cup of honey as a unit rate.

Alfonso borrowed $750 from the bank with 4% simple interest and borrowed $1,750 from the bank with 3.5% simple interest.

How do we calculate the amount borrowed?

Let:

x = amount borrowed from the bank that charged 4% simple interest

y = amount borrowed from the bank that charged 3.5% simple interest

Therefore, we have:

x + y = 2,500 ............................... (1)

0.04x + 0.035y = 91.25 ............................. (2)

From equation (1), we have:

x = 2,500 - y ....................... (3)

Substituting equation (3) into (2) and solving for y, we have:

0.04(2,500 - y) + 0.035y = 91.25

100 - 0.04y + 0.035y = 91.25

100 - 0.005y = 91.25

-0.005y = 91.25 - 100

-0.005y = -8.75

y = -8.75 / -0.005

y = $1,750

Substituting for y in equation (3), we have;

x = 2,500 - 1,750

x = $750

Learn more about the amount borrowed here: brainly.com/question/17619427.

#SPJ

Answer: 12 different even 2 digit positive numbers can be witten

Step-by-step explanation:

the even numbers are 44, 24, 54, 84, 22, 42, 52, 82, 28, 48, 58, 88

Modelling the situation, it is found the price of the ticket without the coupon is of $9 when all the six friends spent $ 42 to buy the tickets.

Total money spent by 6 friends on purchasing of the movie tickets = $ 42

So, the money spent for the purchase of 1 ticket will be calculated by dividing the $ 42 by 6.

So, cost of 1 ticket = 4 42 / 6 = $ 7

Coupon is of $2-off.

This means that with the coupon, $2 is subtracted from the ticket price.

So, price of ticket will be = $ 7 + $ 2 = $ 9.

Therefore, the price of the ticket without the coupons will be $ 9.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ9

The rent option will cost 120 more dollars than the outright cost of the computer .

The outright cost of the computer is $864.

The store also offers a rent to own option which will cost $41 per week for 24 weeks.

Therefore, the total cost for the rent option is as follows:

cost of the computer for rent option = 41 × 24

cost of the computer for rent option = 984 dollars

Therefore,

difference in cost = 984  - 864

difference in cost = 120 dollars

Therefore, the rent option will cost 120 more dollars than the outright cost of the computer.

learn more on cost here: https://brainly.com/question/15776777

#SPJ1

Answer:

This is the answer :20 5/6 and 102.2

Answer: see explanation

Step-by-step explanation:

The 10 cm distance is measured perpendicularly to the chord, forming a right angle and bisecting the chord. Thus half of the chord, the segment from the center of the chord, and a radius to the end of the chord form a right triangle. The hypotenuse is 26 cm and one leg is 10 cm, so the other leg is given by the Pythagorean theorem: a^2 + 10^2 = 26^2, giving a = 24 cm. Since a is half the chord, the chord is 2a = 48 cm in length.

Hence, the length of a chord of a circle is [tex]48cm[/tex].

What is the circle?

A circle is defined as a two-dimensional figure, which is round in shape where all the points on the surface of the circle are equidistant from the center point is called “[tex]P[/tex]”.

Here given that,

A circle of radius [tex]26[/tex]cm if the chord is [tex]10[/tex]cm from the center of the circle.

So,

The  [tex]10[/tex]cm from the center of the circle is perpendicular of the chord and the hypotenuse is  [tex]26[/tex]cm .

As we know

[tex]H^2=B^2+P^2[/tex]    .......[tex](1)[/tex]

Substituting the values in the equation [tex](1)[/tex], we get

[tex](26)^2=(10)^2+B^2\\B^2=676-100\\B^2=576\\B=\sqrt{576}\\B=24cm[/tex]

Hence, the length of a chord of a circle is [tex]48cm[/tex].

To know more about the circle

https://brainly.com/question/266951

#SPJ2

Answer:

it is x=8 or x=-8

Step-by-step explanation:

|x|-7=1

  +7 +7

x=8 or x=-8

i'm doing absolute value in math rn so this should be right!! have a good day

The expression which has the same value as the given expression; 4² - 6 × 2 among the answer choices is; Choice C; 10 - 3 x 2 + 4¹.

According to the task content; the given expression whose equivalent is to be determined is;

Given;

4² -6 ×2.

It follows from PEMDAS that the exponent should be evaluated and then the multiplication.

Hence, the value of the expression is; 16 - 8

= 8.

For answer choice C, which is correct, the evaluation is as follows;

10 - 3 × 2 + 4¹

= 10 -6 + 4

= 8.

Ultimately, choice C has the same value as the given expression.

Read more on PEMDAS;

https://brainly.com/question/11258067

#SPJ1

Answer:

64,765

Step-by-step explanation:

multiplicas porque dice que uno cuesta 315 entonces si hay 205 hay 64,765

-5 and 7 are real and rational numbers also they are integers.

Numbers which can be written in the form of p/q are rational numbers where q must not be zero.

According to the given question we have to determine what kind of numbers are -5 and 7.

In a most simple way we can say that - 5 is an negative integer and 7 is a positive integer.

But -5 can be written as -5/1 which is a rational number also and 7 can also be written as 7/1 so we can also say they are integers al well as rational numbers.Lastly they are real numbers as they don't have any imaginary part 'i' in it.

learn more about rational numbers here :

https://brainly.com/question/24398433

#SPJ1

The slope-point form is y + 1 = (1/4) (x +2)

The function notation for the point-slope form is f(x) = -1 + (1/4) (x +2)

From the graph, we get two points (x₁, y₁) = (-2, -1) and (x₂, y₂) = (2,0)

Slope, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{0 --1}{2--2}[/tex]

               = 1/4

The slope-point form of a line is (y-y₁) = m(x-x₁), where (x, y) is the general point on the line, (x₁, y₁) is a given point on the line and m, the slope of the line.

So here the slope-point form of the line is,

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

⇒ y + 1 = (1/4) (x +2)

For the function notation, we put y = f(x) simply and write it as,

f(x) = -1 + (1/4) (x +2)

Learn more about slope-point form of a line at https://brainly.com/question/6497976

#SPJ9

the first one is c

the second is B

Step-by-step explanation:

The slope of a linear demand curve is negative

The demand curve's negative slope indicates that there is an inverse link between price and demand.

It is true that the demand curve's negative slope indicates an inverse link between price and quantity desired. According to the demand curve, demand declines as prices increase and rises as prices decrease.

This statement is false since it only applies to Giffen products, where the demand curve has a positive slope and a direct correlation between price and quantity desired.

Because unit requests rise when prices decrease and decline when prices rise, the demand curve often slopes downward (i.e., is negative). Demand increases when prices are low, but demand decreases when prices are high.

Learn more about demand curve here

https://brainly.com/question/1139186

#SPJ9

Answer: 0.48387

Step-by-step explanation:

Solution set = {9,11,13,15,17,19,21,23,25,27,29,31,33,35,37}

Sample Set = {8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38}

out of the 31 numbers, 15 are odd

15/31 = 0.48387 probability.

Answer:

64.75

Step-by-step explanation:

The total heights of men is m

so m/15 = 69.65 => m = 1044.75

The total heights of all students is s

so s/35 = 66.85 => s = 2339.75

so the total heights of women = 2339.75 - 1044.75 = 1295

The mean height of women = 1295/20 = 64.75

Answer:

38363

Step-by-step explanation:

The days it would take to complete the building is 104 22/25 days.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.

The first step is to determine the total height of the office bulding = height of each floor x total number of floors

15 x 10 2/5

15 x 52/5 = 780 /5 = 156

The next step is to determine the floors left to complete the office building :

156 - 24 9/10 = 131 1/10 feet

The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :

1311/10 ÷ 1 1/4

1311 / 110 ÷ 5/4

1311 / 10 x 4/5 = 104 days 44/50

104 22/25 days

To learn more about the division of fractions, please check: https://brainly.com/question/25779356

#SPJ1

The set of ordered pairs that represents a function is the third option.

{ (4, 1), (-6, 6), (5, -2), (-4, 1)}

For a relation that maps elements x (inputs) into elements y (outputs), we will have ordered pairs of the form (x, y) that define the relation.

Now, a relation is only a function if input are only mapped to only one output.

For example, if you look at the first set of ordered pairs, you can see that the input x = -4 appears twice with two different outputs, then this relation does not represent a function.

For the second set the same thing happens for the input x = -8, and for the last set the same happens for the input x = -8

The only set where each input appears only once is the third one:

{ (4, 1), (-6, 6), (5, -2), (-4, 1)}

This relation represents a function, so this is the correct option.

If you want to learn more about functions:

https://brainly.com/question/2328150

#SPJ1

Answer:

in the heaven or hell hhhvgvcgdgghh

we get that, the value of x for the given angles in the diagram is 10°.

We can see that:

∠  NMG + ∠ GML = ∠ NML

Substituting the values of the angles in the equation, we get that:

46 ° + 8 x - 5° = 11 x + 11 °

Combining the like terms:

8 x + 41° = 11 x + 11°

Taking variables on one side:

11 x - 8 x = 41° - 11°

Combining the like terms again:

3 x = 30°

Divide both sides by 3:

x = 30° / 3

x = 10°

Therefore, we get that, the value of x for the given angles in the diagram is 10°.

Learn more about angles here:

https://brainly.com/question/25716982

#SPJ9

Your question was incomplete. Please refer the content below:

∠ NMG = 46°, ∠ NML = 11x + 11, and ∠ GML = 8x-5. Find x.​

Answer: 1/4

Step-by-step explanation:

The easiest way to solve this is to make them all common denominators.

The common denominator for this problem is 24.

Change the denominators:

1/4  = 6/24

4/12 = 8/24

3/8 = 9/24

2/6 = 8/24

This way it is easier to see which one is smaller and closest to 0. In this case, it is 6/24 or 1/4 because 6/24 is the smallest out of all of them.

Answer:

Your answer is x=0

Answer:

4

Step-by-step explanation:

[tex] \frac{(2 {)}^{3}(2 {)}^{4} }{(2 {)}^{5} } [/tex]

→[tex] {2}^{3 + 4 + 5} [/tex]

→[tex] {2}^{2} = 4[/tex]

The 4 on the right is 10 times larger than the 4 on the left! (=^.^=)

Answer:

1. 1, 9/4

2. 4^4

3. -0.0000000008723

4. -5100023*10^2, -6.6*10^(12)

Step-by-step explanation:

[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]

Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.

-8.723 * 10^-10 would be -0.0000000008723.

10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.

[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]

Answer:

3.82×10^7

Step-by-step explanation:

3.82e+7= 3.82×10^7

Using integrals, the volume generated by rotating the given region about the specified line is of 0.8π cubic units.

Rotating a function f(x) around a function g(x), the volume is given by the following integral:

[tex]V = \pi \int_{a}^{b}[f(x) - g(x)]^2 dx[/tex]

In which a and b are the intersection points of the curve.

For this problem, from the graph, we have that:

Hence:

[tex]V = \pi \int_{0}^{1}[2\sqrt[4]{x} - 2x]^2 dx[/tex]

[tex]V = \pi [\int_{0}^{1} 4\sqrt{x} - 8x\sqrt{x} + 4x^2 dx][/tex]

[tex]V = \pi \left[\frac{8}{3}x^{\frac{3}{2}} - \frac{16}{5}x^{\frac{5}{2}} + \frac{4}{3}x^3}\right]_{x=0}^{x=1}[/tex]

[tex]V = \pi \left[\frac{8}{3} - \frac{16}{5} + \frac{4}{3}\right][/tex]

[tex]V = \pi \left[4 - \frac{16}{5}\right][/tex]

[tex]V = \frac{4\pi}{5}[/tex]

V = 0.8π cubic units.

More can be learned about integrals and volumes at https://brainly.com/question/18371476

#SPJ1

The sample space for the event is given by {2,3,4}

The sample space is a collection of all possible outcomes of an experiment. The sample space is used in probability where the it represents all possible outcomes.

a) In the spinner there are only three possibilities.

The sample space is represented by  {2,3,4} .

b)The favorable outcomes in this case is  2 and 4.

Hence the number of favorable outcome is 2.

c)There is only 1 unfavorable outcome which is 3.

d)The total number of possible outcomes is 3 , as we see in the sample space there are 3 numbers.

e)The probability is defined as the fraction of favorable outcome to the

total number of outcome. Therefore the probability in this case is given

by  [tex]P(even)=\frac{2}{3}[/tex]

f) The ratio of the number of possible outcomes to the number of possible outcomes that do not occur is known as the odds in favor.

Therefore odds in favor = 2:1

To learn more about sample space visit:

https://brainly.com/question/28043513

#SPJ9