Joaquin has 3/5 cup of drink mix. He puts the same amount of drink mix into each of 5 pitchers. What fraction of a cup of drink mix is in each pitcher?

2y - 3 > -1    |add 3 to both sides

2y > 2     |divide both sides by 2

y > 1

-----------------------------

5 - y > 4      |subtract 5 from both sides

-y > -1      |change the signs

y < 1

y > 1 or y < 1

Let X be the number of weeks she deposits money.

The equation to solve for the account balance would be 120 + 5x ( She started with 120 dollars and is adding 5 dollars per week)

week 1: balance = 120 +5(1) = $125

week 2: balance = 120 +5(2) = $130

week 3: balance = 120 + 5(3) = $135

week 4: balance = 120 +5(4) = $140

Now to see if it proportional divide each total by the number of weeks:

week 1: 125 / 1 = 125

week 2: 130 / 2 = 65

week 3: 135 / 3 = 45

week 4: 140 / 4 = 35

Find the difference between the weeks:

Week 1 & 2 : 125 - 65 = 60

Week 2 & 3: 65 -45 - 20

Week 3 & 4: 45 -35 = 10

Since the 3 differences are not the same, the balance is not proportional to the number of weeks.

Answer:

It is a geometric sequence en the common ratio is: [tex]r=\frac{5}{2}[/tex].

Step-by-step explanation:

1. By definition, a geometric sequence is a sequence in which you obtain a term by multiplying the previous one by a common ratio.

2. The common ratio is obtained by dividing a term by its preceding term.

3. Keeping this on mind, you have:

[tex]\frac{320}{128}=\frac{5}{2}\\[/tex]

[tex]\frac{800}{320}=\frac{5}{2}[/tex]

[tex]\frac{2000}{800}=\frac{5}{2}[/tex]

4. As you can see, the common ratio is [tex]\frac{5}{2}[/tex]

Answer:

2.5!!

Step-by-step explanation:

100% correct

For Mark to buy 20 cookies, it'll cost him about $4.40

The cost of 20 cookies if 12 cookies cost $2.70 is $4.50.

12 cookies cost $2.70

Then,

20 cookies cost $x

Set up the ratio

12 : 2.70 = 20 : x

12/2.70 = 20/x

cross product

12 × x = 2.70 × 20

12x = 54

Divide both sides by 12

x = 54/12

x = $4.50

Therefore, 20 cookies cost $4.50

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Solve for r by simplifying both sides of the equation, then isolating the variable.

Your answer is A.

You can distribute the q to both terms to get

[tex] q(2a+1) = q\cdot 2a + q\cdot 1 = 2aq+q [/tex]

Answer:

2aq +q is an equivalent expression for q(2a+1)

Step-by-step explanation:

an equivalent expression to q(2a+1)

To get equivalent expression we need to multiply q inside the parenthesis

q times 2a = 2aq

q times 1 is q

Now we combine both term

q(2a+1)= 2aq + q

So 2aq +q is an equivalent expression for q(2a+1)

[tex]y=\dfrac{8x+3}{4}=\dfrac{8x}{4}+\dfrac{3}{4}=2x+\dfrac{3}{4}[/tex]

It's a linear function y = mx + b. The domain of linear function is the set of all real numbers.

We have no objections to the value of x. x can be any number.

Therefore your answer is:

a) All real numbers.

50 : 45

10 : 9 (10 yellow : 9 red)

50 yellow and 45 red

The ratio of yellow to red = 50/45 = 10/9

Answer

The ratio of yellow to red is 10/9 or 10:9

Answer:

C. sqrt(95)

Step-by-step explanation:

The three triangles are similar, so you can use the right triangle altitude theorem.

(14 + 5)/m = m/5

19/m = m/5

m^2 = 19 * 5

m^2 = 95

m = sqrt(95)

Answer: C. sqrt(95)

X=11 because

5x+9x+26=180

14x+26=180

14x=154

x=11

Answer:  The required value of x is 11.

Step-by-step explanation:  Given that the lines f and g are parallel to each other.

We are to find the value of x.

From the figure, we note that the parallel lines f and g are cut by a transversal,  and

angles with measures 5x° and (9x+26)° are interior angles on the same side of the transversal.

We know that, if two lines are parallel, then the measures of the angles on the same side of the transversal is 180°.

Therefore, we get

[tex]5x^\circ+(9x+26)^\circ=180^\circ\\\\\Rightarrow 5x+9x+26=18\\\\\Rightarrow 14x=180-26\\\\\Rightarrow 14x=154\\\\\Rightarrow x=\dfrac{154}{14}\\\\\Rightarrow x=11.[/tex]

Thus, the required value of x is 11.

The solution to the inequality 8(1/2x - 1/4) > 12 - 2x is x > 7/3.

To solve the given inequality 8(1/2x - 1/4) > 12 - 2x, first you should distribute the 8 to both terms in the parentheses. This gives you 4x - 2 > 12 - 2x. Next, we need to group like terms, so let's add 2x to both sides of the inequality to obtain 6x - 2 > 12. Afterwards, add 2 to both sides, resulting in 6x > 14. Finally, divide each side by 6 to isolate x, which gives x > 7/3. So, the solution is x > 7/3.

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Answer:

iit =

Step-by-step explanation:

Answer:

A. 16¾

Step-by-step explanation:

We will convert all the mixed fractions to improper fractions.

Monday, 5½ = [tex]\frac{11}{2}[/tex]

Wednesday, 6¾ = [tex]\frac{27}{4}[/tex]

Friday, 4½ = [tex]\frac{9}{2}[/tex]

Now, we will add all these fractions by taking the LCM of denominator.

The LCM of 2,4 and 2 is 4.

We get the following result after addition.

[tex]\frac{11}{2} +\frac{27}{4} +\frac{9}{2}[/tex]

= [tex]\frac{22+27+18}{4}[/tex]

= [tex]\frac{67}{4}[/tex] hours

In mixed fraction it becomes 16¾ hours.

Answer-

a. The engine speed that maximizes torque is 3.1 thousand revolutions per minute  and the maximum torque is 74.68 ft-lbs

b. As the engine speed increases, the torque increases until the engine speed reaches  3.1 thousand revolutions per minute and then the torque decreases.

Solution-

The given equation is,

[tex]y=-3.75x^2+23.2x+38.8[/tex]

Where x = the speed of the engine (in thousands of revolutions per minute)

           y = the engine torque y (in foot-pounds)

a.

In order to calculate the max torque and when it is max, we have to take the help of maxima and minima concepts from application of derivatives.

[tex]\Rightarrow y=-3.75x^2+23.2x+38.8[/tex]

[tex]\Rightarrow {y}'=-7.5x+23.2[/tex]

[tex]\Rightarrow {y}''=-7.5[/tex]

Equating the first derivative to 0, in order to find critical points,

[tex]\Rightarrow {y}'=0[/tex]

[tex]\Rightarrow -7.5x+23.2=0[/tex]

[tex]\Rightarrow x=\frac{-23.2}{-7.5} = 3.093 \approx 3.1[/tex]

As the value of second derivative is negative, hence the value of the function at x=3.1 will be maximum.

The value of max torque is,

[tex]y(3.1)=-3.75(3.1)^2+23.2(3.1)+38.8=74.682 \approx 74.68[/tex]

b.

Calculating the roots of the function,

[tex]\Rightarrow y=0[/tex]

[tex]\Rightarrow -3.75x^2+23.2x+38.8=0[/tex]

[tex]x=-1.369,7.556[/tex]

As these are the roots or x-intercept, the value of the function at these points is zero.

As shown in the graph, the function increases from x=0 to x=3.1 (as the speed can not be negative, so neglecting negative values) and after x=3.1 it decreases.

At about 3093 revolutions per minute, the engine torque reaches its maximum of 44.97 ft-lbs. Prior to this, the torque increases with engine speed, but starts to decrease once the speed surpasses this point.

The equation given is that of a downward opening parabola, which means it has a maximum point. The vertex (h, k) of a parabola given by the equation y = a(x-h)^2 + k is at x = -b/2a. For the given equation, a = -3.75 and b = 23.2.

Substituting these values, we get x = -23.2/(2*-3.75) = 3.093 to the nearest thousand, which translates to 3093 revolutions per minute. Substituting this value of x in the equation gives the maximum torque y = -3.75*(3.093)^2 + 23.2*3.093 + 38.8 = 44.97 ft-lbs to the nearest hundredth.

As the engine speed increases, the torque increases until the engine speed reaches about 3093 revolutions per minute. After this, "the torque then starts to decrease".

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1. D

2. D

I don't know the answer to number 3 sorry.

Answer with explanation:

1. x+0=x

0 is the identity element.When number is added to identity the resultant is number.

Option D : Identity

2.

3x-2=60

Adding 2 on both sides

→3x-2+2=60+2

→3x=62

Dividing by 3, on both sides

[tex]x=\frac{62}{3}[/tex]

Option (B.)→ Add 2 . Divide by 3

3.

y> -2,

y=(-2, Infinity)

So, -3 is not the solution of ,y>-2.

Option A: False

4.

The equation in slope-intercept form, is, y = mx + b.

4x-2y=10

4x=2y+10

2y=4x-10

Dividing by 2, on both sides

y=2x-5

Option A:→y=2x-5

5.

The equation of line is

 y=2x-11

We have to check whether point (3,0) lies on the line or not.

LHS=y=0

RHS=2x-11

       =2 ×3-11

       =6-11

       = -5

So, point (3,0) does not lie on the line,→y=2x-11.

Option B : False

6.

Slope of line joining the points (-2,-1) and (3,4) is

 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m=\frac{4+1}{3-(-2)}\\\\m=\frac{5}{5}\\\\m=1[/tex]

Slope=1

Option A

7.

When solving a system of equations, you are finding the

Option C: Intersection point

8.

[tex]3x + 2y = 10------(1) \\\\2x + 3y = \frac{15}{12}-----------(2)\\\\1+2\\\\5x+5y=\frac{135}{12}\\\\x+y=\frac{27}{12}-----(3)\\\\1-2\\\\x-y=\frac{105}{12}-----(4)\\\\ 3+4\\\\2x=\frac{132}{12}\\\\2x=11\\\\x=\frac{11}{2}\\\\y+\frac{11}{2}=\frac{27}{12}\\\\y=-\frac{11}{2}+\frac{27}{12}\\\\y=\frac{-39}{12}[/tex]

Total cost of the purchase by Barry is given by the equation A = $ 36 and the amount saved by Barry is $ 14

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of all the purchase by Barry be A

Now , the equation will be

The cost of the sweater = $ 50

The marked down percentage of sweater = 20 %

So , the new cost of the sweater = cost of the sweater - ( marked down percentage x cost of the sweater )

Substituting the values in the equation , we get

The new cost of the sweater = 50 - ( 20/100 ) x 50

The new cost of the sweater = 50 - 10

The new cost of the sweater = $ 40

Now , the coupon discount percentage = 10 %

So , the final cost of the purchase A = new cost of the sweater - ( coupon discount percentage x new cost of the sweater )

Substituting the values in the equation , we get

The final cost of the purchase A = 40 - ( 10/100 ) x 40

The final cost of the purchase A = 40 - 4

The final cost of the purchase A = $ 36

So , the amount saved by Barry = cost of the sweater - final cost of the purchase

The amount saved by Barry = 50 - 36 = $ 14

Hence , the cost of the sweater is $ 36

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Answer:

Value of house before Increase = $700000.

Step-by-step explanation:

Let the value of house before increase be $x.

Increase in value = 7%of x= .07x

Value of house before increase+ Increase in value = Total value.

x+.07x=749000

Adding like terms,

1.07x=749000

Dividing both sides by 1.07.

x=700000.

Value of house before Increase = $700000.

Answer:

Zoe counted 20 more black kittens than white kittens.

Step-by-step explanation:

Let the white kittens be = x

Then the black kittens be = 4x

Zoe counts a total of 25 kittens.

So, we get;

[tex]x+2x=25[/tex]

=> [tex]5x=25[/tex]

Dividing both sides by 5, we get;

x = 5

White kittens are = 5

Black kittens are = [tex]4\times5=20[/tex]

So, the black kittens are [tex]25-5=20[/tex] more than white ones.

Therefore, Zoe counted 20 more black kittens than white kittens.

Answer: Simple Random Sampling (SRS)

The people chosen are basically picked out of a hat at random, though likely they are chosen by a computer.

Answer:

Random cell phone calls sent out to a sample size of 850 people would typically be considered a form of random sampling. However, the specific type of random sampling can vary. It could be simple random sampling if each person in the population has an equal chance of being called, and the selection is done entirely by chance, such as using a random number generator to select phone numbers.

Alternatively, it could be stratified random sampling if the population is divided into different groups or strata (e.g., age groups, geographic regions), and then random samples are taken from each stratum in proportion to its size.

The exact method used depends on the sampling strategy and goals of the study, but as long as the selection of individuals is based on randomness and each person has an equal chance of being included, it falls under the broad category of random sampling.

Step-by-step explanation:

Erika will spend $60 on cupcakes for the 20 guests at her party by purchasing one $3 cupcake for each guest.

To calculate how much Erika will spend on cupcakes for the party, we need to multiply the number of guests by the cost of each cupcake. Each guest will get one cupcake, and since there are 20 guests, we need 20 cupcakes. The cost of one cupcake is $3.

To find the total cost, we perform the following calculation:

Therefore, Erika will spend $60 on cupcakes for the party.

No. A parallelogram has 2 sets of parallel lines, each the same length. This doesn't mean that the angles are perpendicular.

Answer:

a is the middle point on x-axis = 3

Step-by-step explanation:

On probability distribution graph, P(x≥a) means area under the curve from x=a to x=6.

On a probability distribution graph, the entire area under curve =1

But we are given that P(X≥a) is 0.5 which is half of 1.

And we are given with a normal distribution graph which has center at x=3.

Hence half of the area means area from x=3 to x=6 which is nothing but P(X≥3).

Therefore a is 3.

We can also check it by finding area under curve from x=3 to x=6.

Area under curve from x=3 to x=6 can spitted into a rectangle and a triangle.

Rectangle area = (5-3)X0.2=0.4

Triangle area=[tex]\frac{1}{2}X0.2X1=0.1[/tex]

Hence total area from x=3 to x=6 is 0.4+0.1=0.5

we know that

The Angle of Depression. is the angle below the horizontal that an observer must look to see an object that is lower than the observer

in this problem

the angle  below the horizontal is the angle C

therefore

the answer is

The angle of depression is the angle C

Answer:

75 pages

Step-by-step explanation:

The first Graph is correct.

Hope This Helped!

;D

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We know that a ray is a line that has one end point and extends infinitely from the other end.

i.e. it is a line that originates at a point and goes to infinity.

Now, it is given that:

A ray has one point at a given distance from the endpoint of the ray.

The graph that describes this statement is attached to the answer.

( while the other graph describes that there is a line that passes through the line segment AB.

Since it extends to infinity in both the direction )