Dana is buying Grandparents' Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends 4/5 of that on a coffee mug for her grandfather. How much money does Dana spend in all?

Answer:

There are two equations and two variables, so this is a system of linear equations.

c + h = 360

4c = h

Step-by-step explanation:

Answer:

The linear equations would be c = 4h and 1.5c + 2h = 360.

Step-by-step explanation:

First we have to create a table for our data.

c = total number of cold beverages sold.

h = total number of hot beverages sold.

The total cost of both beverages sold -

1.5c + 2h = 360

The amount of cold beverages -

c = 4h

Now we just need to substitute the second equation to the first one.

1.5 * (4h) + 2h = 360

= 6h + 2h = 360

= 8h = 360

= h = 45

Now we need to find the value of c.

c = 4* 45 = 180

Therefore 180 cold beverages were sold and 45 hot beverages were sold.

But the linear equations would be c = 4h and 1.5c + 2h = 360.

Hope this helped! :D

Answer:

f(x) = -2x - 3

g(x) = -2x³ - 5

f(5) = -2(5) - 3

f(5) = -10 - 3

f(5) = -13

g(-2) = -2(-2)³ - 5

g(-2) =-2(-8) - 5

g(-2) = 16 - 5

g(-2) = 11

Answer:

the answer should be 9

Step-by-step explanation:

,look at a graph count from 0,-6 up to 0,3 . the distance between them is 9

Answer: 9

Step-by-step explanation:

let the two points P (0,3) and Q(0,-6)

We need to find distance PQ

PQ=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

here

x1=x coordinate of P=0

y1=y coordinate of P=3

x2=x coordinate of Q=0

y2=y coordinate of Q=-6

Putting values

 [tex]PQ=\sqrt{(0-0)^2+(-6-3)^2}\\[/tex][tex]PQ=\sqrt{(0)^2+(-9)^2} \\PQ=\sqrt{81} \\PQ=9[/tex]

Answer:

196cm²

Step-by-step explanation:

14*14=196

area = length of one side * the length of the other side

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads:}[/tex]

[tex]\large\textbf{Which is equivalent to }\rm{\bf \dfrac{3}{125}}\large\textbf{ ?}[/tex]

[tex]\huge\textbf{Solving for your fraction:}[/tex]

[tex]\mathbf{\dfrac{3}{125}}[/tex]

[tex]\mathbf{= \dfrac{3\times2}{125\times2}}[/tex]

[tex]\mathbf{\approx \dfrac{3 + 3}{125 + 12{5}}}[/tex]

[tex]\mathbf{= \dfrac{6}{250}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\dfrac{6}{250}}}\huge\checkmark[/tex]

[tex]\large\text{By the way, they are a lot more fractions that are equivalent to}\\\large\text{the given equation (}\rm{\dfrac{3}{125}}\large\text{) but we only labeled one that is the very}\\\large\text{first fraction that is equal to it. }[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Step-by-step explanation:

sin^-1√-3/2=300°

cos300°=0.5

Answer:

42.0 ft

Step-by-step explanation:

let t be the height of the tree.

At the same time ,the measure of something

and its shadow are proportional .

Then

[tex]\frac{2}{6} =\frac{14}{t}[/tex]

Then

2t = 6 × 14

Then

2t = 84

Then

t = 84/2

Then

t = 42

Therefore the tree is 42 ft tall

The length of AB would be 38 units

The attached image represents the missing piece in the question

Considering the triangle BCD;

Calculate the length BC using the following Pythagoras theorem

BC^2 = CD^2 + BD^2

This gives

BC^2 = 10^2 + 8^2

Evaluate

BC^2 = 164

Considering the triangle CBA;

Calculate the length AB using the following Pythagoras theorem

AB^2 = AC^2 - BC^2

This gives

AB^2 = 40^2 - 164

Evaluate

AB^2 = 1436

Take the square root

AB = 38 (approximated)

Hence, the length of AB would be 38 units

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Answer:     0

Step-by-step explanation:

Answer:

34352.0

Step-by-step explanation:

The ride takes  1.5 hours for a speed of 10 miles per hour.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

A body's speed can be defined as how quickly it is going. The equation for a given body's speed can be written as,

Speed=Distance/Time

According to the question,

Speed=10 miles per hour

Distance=15 miles

Time=[tex]\frac{15}{10}[/tex]=1.5 hours

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Answer:

708π in³ = 2224.25 in.³

Step-by-step explanation:

The composite solid is made up of a cone, a cylinder, and a half sphere.

Recall the volume formulas:

cone: πr²h/3

cylinder: πr²h

sphere: 4πr³/3

half sphere: (1/2) × 4πr³/3

We need to find teh heoght of the cone. The slant height is 10 in. The radius is 6 in. We can use the Pythaogorean theorem to find the height of the cone.

h = √(10² - 6²) = 8

total volume = π(6 in.)²(8 in.)/3 + π(6 in.)²(13 in.) + (1/2) × 4π(6 in.)³/3

total volume = π(96 in.³ + 468 in.³ + 144 in.³)

total volume = 708π in³ = 2224.25 in.³

The fourth proportionals are bc/a and st/r

Segments a, b and c

Let the fourth segment be x.

So, we have the following equivalent ratio

a : b = c : x

Express as fraction

a/b = c/x

Make x the subject

x = bc/a

Segments r, s and t

Let the fourth segment be x.

So, we have the following equivalent ratio

r : s = t : x

Express as fraction

r/s = t/x

Make x the subject

x = st/r

Hence, the fourth proportionals are bc/a and st/r

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The rate of change of the relationship is 6/5

The rate of change of a line is also known as the slope of the line. The formula for calculating the slope of a line is expressed as:

Slope =y2-y1/x2-x1

Given the coordinate points (-3,-2) and (2, 4). On substituting;

Slope = 4-(-2)/2-(-3)

Slope =4+2/2+3

Slope = 6/5

Hence the rate of change of the relationship is 6/5

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The exponential function is often used to model the growth or decay of a population

The population size of the yeast cell after 3 hours is 6.24 million

The given parameters are:

a = 3.1M --- initial number of cells

r = 0.4425 per hour --- rate

The nth term of an exponential function is:

f(n) = a(1+r)^n-1

After 3 hours; n = 3

So, we have:

f(3) = a(1+r)^3-1

Substitute values for a and r

f(3) = 3.1 (1+0.4425)^3-1

f(3) = 3.1 ( 1.4425)^2

f(3) = 6.24

Hence, the population size of the yeast cell after 3 hours is 6.24 million.

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The volume of the sphere shown below with a radius of 9 is 3052.08 cubic units

The formula for calculating the volume of a sphere is expressed as;

V = 4/3πr³

where

r is the radius of the sphere

Substitute

V = 4/3π(9)³

V = 4/3(3.14)*729

V = 3052.08 cubic units

Hence the volume of the sphere shown below with a radius of 9 is 3052.08 cubic units

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Using the normal distribution, it is found that 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the amounts are given as follows:

[tex]\mu = 3456, \sigma = 478[/tex]

The proportion is the p-value of Z when X = 4250, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4250 - 3456}{478}[/tex]

Z = 1.66

Z = 1.66 has a p-value of 0.9515.

Hence 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.

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Answer:

1-0.07/100*7=0.9951

The cosine model is y = - 7 + 10 · cos (π · x/30 - π).

The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).

Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:

[tex]y = A \cdot \cos (B\cdot x + C) + D[/tex]     (1)

[tex]y = A\cdot \sin (B\cdot x + C) + D[/tex]      (2)

Where:

First, we find the amplitude and the midpoint:

A = [3 - (- 17)]/2

A = 10

D = [3 + (- 17)]/2

D = - 7

Now we find the angular phase and the angular frequency for each model:

Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)

- 17 = 10 · cos C - 7     (3)

3 = 10 · cos (30 · B + C) - 7      (4)

By (3):

- 10 = 10 · cos C

cos C = - 1

C = acos(- 1)

C = - π

And by (4):

3 = 10 · cos (30 · B - π) - 7

10 = 10 · cos (30 · B - π)

cos (30 · B - π) = 1

30 · B - π = acos 1

30 · B - π = 0

30 · B = π

B = π/30

The cosine model is y = - 7 + 10 · cos (π · x/30 - π).

Sine model

Obtain the sine model by using trigonometric expressions:

cos θ = sin (θ + π/2)     (5)

By (5):

y = - 7 + 10 · sin (π · x/30 - π + π/2)

y = - 7 + 10 · sin (π · x/30 - π/2)

The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).

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The average selling price per box is $5.33

The core value of a set of data is expressed as the average of a list of variables. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. The average of a specific set of numerical data is also known as the mean in statistics.

Average = Sum of Values/Number of Values

The total selling price of all boxes=(8*100)+(800*6)+(600*4)

                                                   =$8000

Total number of boxes=100+800+600

                                      =1500

Average selling price per box=8000/1500=$5.33

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Answer:

first type: 144 pints

second type: 36 pints

Step-by-step explanation:

So let's try to interpret the given information. So the first thing to know is how to calculate x%, to calculate this, you simply multiply the number by x/100, which is what x is in decimal form.

So let's just start off by assigning variables to each brand, with the variable representing the amount of pints. Let's say "x" is the amount of pints of the first brand, and "y" is the amount of pints of the second brand.

The next thing to do is make equations using the given information. So we want a fruit drink that is 55% pure fruit juice, and it's 180 pints. So to find what 55% is, we multiply by 55/100 or 0.55. This means that 55% is 0.55(180) = 99. So using the given information this means that 99 pints is pure fruit juice in the mixture. This comes from mixing the first two brands, so that means if we take the pure fruit juice from the first brand and add it to the second brand we get 99, and remember we are given the information that 45% of the first brand is pure fruit juice and the second is 95%, this means that 0.45x is pure fruit juice in the first brand and 0.95y is pure fruit juice in the second brand. This sets up the following equation: [tex]99 = 0.45x + 0.95y[/tex]

The second equation to set up is using the total amount of pints. x represents how much is from the first brand, and y represents how much is from the second brand. Since the mixture consists of these two brands, and the mixture is 180 pints we can form the equation: [tex]180 = x+y[/tex]

The last step is to solve the systems of equations using the two equations we formed. This can be done via substitution. We simply need to solve for either x or y, in the total amount of pints equation and then substitute it into the pure fruit juice equation. In this example I'll solve for x

Original Equation:

[tex]180 = x+y[/tex]

Subtract y from both sides

[tex]180-y=x[/tex]

So now that we solved for y in terms of x we can substitute this into the pure fruit juice equation, so that we're only dealing with one variable.

Original Equation:

[tex]99 = 0.45x + 0.95y[/tex]

Substitute 180-y as x

[tex]99 = 0.45(180-y) + 0.95y[/tex]

Distribute the 0.45

[tex]99=81-0.45y+0.95y[/tex]

Add like terms

[tex]99=81+0.5y[/tex]

subtract 81 from both sides

[tex]18=0.5y[/tex]

Divide both sides by 0.5 (same thing as multiply by 2)

[tex]36=y[/tex]

This means we have to use 36 pints of the second brand. We can substitute this into either equation to solve for x, but it's easier to substitute into the total pints equation since there are no coefficients (technically a 1 in front, but it's kind of be ignored for now), so it's pretty straightforward to solve for x

Original Equation:

[tex]180=x+y[/tex]

Substitute 36 as y

[tex]180=x+36[/tex]

Subtract 36 from both sides

[tex]144=x[/tex]

This means 144 pints from the first brand and 36 from the second

Sir Yesuba took Rs 1600 from the bank.

Concept : Addition and subtraction from an unknown quantity which can be calculated easily using variables.

Given: The Amount given to son = 3/8x

The Amount given to daughter = 1/4x

Money left = Rs 600

Let the amount taken by him be equal to Rs x.

The Amount given to son = 3/8x

The Amount given to daughter = 1/4x

x - (3/8x + x/4) = 600

x- x/8 = 600

7x/8=600

x= Rs1600

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Answer:

The x and y intercept are (20,0)

Step-by-step explanation:

2x-4y=40—eqn1

-x+2y=-20—eqn2

Make x the subject of eqn2

-x=-20-2y

x=20+2y

plug this into eqn 1

2(20+2y)+4y=40

40+4y+4y=40

8y=40-40

y=0

plug y=0 into eqn2

-x+2(0)=-20

-x=-20

x=20

Answer:

2a+2b

Step-by-step explanation:

3a - a = 2a

4b - 2b = 2b

Answer:

2a+2b

Step-by-step explanation:

3a – a + 4b – 2b

Combine like terms

3a-a =2a

4b-2b =2b

3a – a + 4b – 2b. = 2a+2b

Answer:

bro wuts da answer am so lost yo

Answer: It's my understanding that the answer would be the last one - No, the container is not large enough.....new container is 960 cubic inches. I saw this answer marked on another website but not how to find the answer.

Step-by-step explanation:

Answer:

its easy

Step-by-step explanation:

you should change all into degrees

The country will achieve a blue PPC.

The Production Possibilities Curve (PPC) Sometimes called the production possibilities frontier (PPF) is a model used to show the tradeoffs associated with allocating resources between the production of two goods. The PPC can be used to illustrate the concepts of scarcity, opportunity cost, efficiency, inefficiency, economic growth, and contractions.

Due to the increase in resources of the country, the production capacity for both pineapple & coconut will increase as a result country's PPC will shift rightward/forward. And the country will achieve blue PPC.

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The elements of (A n B)' are ( 3, 4 , 5 ,6). Option A

The elements of this set (A n B) explains the common elements  of both sets without repetition

Set A = 3, 4

Set B = 5, 6

A n B = 1, 2

(A n B)' = Is the elements both A and B in common but is not found in the universal set

(A n B)'  = ( 3, 4 , 5 ,6)

Thus, the elements of (A n B)' are ( 3, 4 , 5 ,6). Option A

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The solution to the given inequality is; x ≥ -9/4 or x ≥ 1

We want to solve the inequality;

(4x² + 5x - 9)/(x² - x - 6) ≥ 0

Let us factorize both numerator and denominator to get;

4x² + 5x - 9 = (4x + 9)(x - 1)

Similarly, x² - x - 6 when factorized gives;

x² - x - 6 = (x + 2)(x - 3)

Thus, we now have;

[(4x + 9)(x - 1)]/[(x + 2)(x - 3)] ≥ 0

Multiply both sides by [(x + 2)(x - 3)] to get;

(4x + 9)(x - 1) ≥ 0

Thus;

(4x + 9) ≥ 0 or (x - 1) ≥ 0

Thus;

x ≥ -9/4 or x ≥ 1

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Answer:

Yes

Step-by-step explanation: