Joanna went school supply shopping. She spent $33.33 on notebooks and pencils. Notebooks cost
$1.85 each and pencils cost $1.39 each. She bought a total of 21 notebooks and pencils. How many of
each did she buy?

Divide price by quantity of each and compare:

7.80 / 12 = o.65 per tin

4.20 / 6 = 0.70 per tin

12 for 7.80 is less per tin, so is the Best Buy.

Answer:

0.89

Step-by-step explanation:

First, let’s find out what one tomato costs. To do this, we need to find the unit rate.

To find the unit rate, divide the cost by the number of tomatoes.

cost/number of tomatoes

It costs $3.55 for 24 tomatoes.

cost=3.55

number of tomatoes=24

Substitute these values in.

3.55/24

0.147916666666667

Each tomato costs $0.147916666666667

Now, we have to find out what 6 tomatoes cost.

Multiply the number of tomatoes by the cost of one tomato

number of tomatoes * cost of one

number of tomatoes=6

cost of one= 0.147916666666667

Substitute these values in.

6* 0.147916666666667

0.8875

Round to the nearest cent or hundredth.

The 7 in the thousandth place tells us to round the 8 in the hundredth place up to a 9.

0.89

6 tomatoes will cost about 0.89.

Answer:

x=0 or x=3 or x= -3⅘

Step-by-step explanation:

Please see attached picture for full solution.

Another way to solve it is to factorise x out from the equation from the beginning. This would leave you with

x(5x² +4x -57x)=0

Then you can factorise the quadratic equation.

x(x -3)(5x +19)= 0

And solve it just like we did above.

x=0 or x-3=0 or 5x+19=0

x=3 or 5x= -19

x= -3⅘

In the picture, I used synthetic division but long division works too!

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the population mean of three-circle red-on-white sheds is equal to the four excavation sites.

To compare the population means you have to apply an ANOVA. For this test the variable of interest is

X: number of  three-circle red-on-white sheds.

There is only one factor: "Site" with four treatments "I, II, III; IV"

H₀: μ₁= μ₂= μ₃= μ₄

H₁: At least one population mean is different.

α: 0.05

[tex]F= \frac{MS_{Treatment}}{MS_{Error}} ~~F_{K-1;N-K}[/tex]

Df treatments: k-1= 4-1= 3 (k= nº of treatments)

Df errors: N-K= 21-4= 17 (N= total observations for all treatments)

[tex]F_{H_0}= \frac{102.72}{117.08}= 0.88[/tex]

p-value: 0.4723

Using the p-value approach the decision rule is:

p-value ≤ α, reject the null hypothesis.

p-value > α, do not reject the null hypothesis.

The p-value is greater than the level of significance, the decision is to reject the null hypothesis.

Using a 5% significance level, there is not significant evidence to reject the null hypothesis. Then you can conclude that the population mean three-circle red-on-white sherd count is equal to all the excavation sites.

I hope this helps!

Answer:

BC = 67

Step-by-step explanation:

Since both tangents are originating from a single point, they are equal, rest in the attached file

Answer:

[tex] 3.45 \times {10}^{11} [/tex]

Step-by-step Explanation:

[tex]345,000,000,000 = 3.45 \times {10}^{11} \\ [/tex]

Answer:

D

Step-by-step explanation:

The equations are similar and so if we compute the vertex we would see they are the same..

Let's try computing the maximum or minimum point of y= -3(x+2)^2 - 4 and y= 3(x+2)^2 - 4 ;

For y= 3(x+2)^2 - 4 ;

to compute the maximum or minimum point we find dy/dx of the expression equating it to 0; the value of x is determined and we substitute to the original expression for y.

If y is -ve we know it's a minimum graph and if y is +be it's a maximum graph.

From the foregoing;

For y= 3(x+2)^2 - 4 ;

dy/dx = 2× 3 ( x+2) ×1 = 6(x+2) = 6x + 12= 0

6x= -12=>x= -12/6= -2;

We substitute x= -2 in y =3(x+2)^2 - 4; y = 3(-2+2)^2-4 = -4

Since y = -4 is a hence y= 3(x+2)^2 - 4 is a minimum graph.

For y= -3(x+2)^2 - 4 ;

dy/dx = 2× -3 ( x+2) ×1 = -6(x+2) = -6x - 12= 0

-6x= 12=>x= -12/6= -2;

Substituting in the y= -3(x+2)^2 - 4 ;

We have;

We substitute x= -2 in y =-3(x+2)^2 - 4; y = -3(-2+2)^2-4 = -4

y= -4 ;

Since both graphs look like they are minimum that is the vertex is y= -4;

Let's explore a further step

The derivative of the previous derivative;

For y= 3(x+2)^2 - 4;

We means d/dy × [dx/dy] = d/dy [ 6x + 12 ] = 6

Hence y= 3(x+2)^2 - 4 is a maximum graph;

Similarly for y= -3(x+2)^2 - 4 ;

d/dy × [dx/dy]

d/dy [-6x-12 ] = -6

Hence y= -3(x+2)^2 - 4 is a minimum graph;

Conclusion: y= 3(x+2)^2 - 4 is a maximum graph and y= -3(x+2)^2 - 4 is a minimum graph;

Answer:

h(n+1) = -⅓ h(n), h(0) = 63

Step-by-step explanation:

h(n) = 63 (-⅓)ⁿ

This is a geometric series where the first term is 63 and the common ratio is -⅓.

Therefore, each term is -⅓ of the previous term.

h(n+1) = -⅓ h(n), h(0) = 63.

Answer:

the answer is c.

Answer:

Let x represent the variety of tickets sold, and y represent the total amount of cash raised. Since each price tag is $2.50, the total amount of money raised is identical to $2.50 instances the wide variety of tickets. The equation would be y = 2.50x.

Step-by-step explanation:

The x variable represents the number of tickets sold.

The y variable represents the total amount of money raised from ticket sales.

The equation for the scenario is y = 2.50x.

Answer:

[tex] 1.3038 \times {10}^{2} [/tex]

Step-by-step explanation:

[tex] (12.3\times 10^8) (1.06\times 10^{-7})\\ = 12.3 \times 1.06 \times {10}^{8} \times {10}^{ - 7} \\ = 13.038 \times {10}^{8 - 7} \\ = 13.038 \times {10}^{1} \\ = 1.3038 \times {10}^{2} [/tex]

Answer:

[tex]1,3038 . 10^{2}[/tex]

Step-by-step explanation:

(12.3 × 10^8)(1.06 × 10^−7)

12.3 × 10^8 × 1.06 × 10^−7

12.3 × 1.06 × 10^8  × 10^−7

10^8  × 10^−7 = 10^(8 -7) = 10^1

12.3 × 1.06 × 10^8  × 10^−7 = 12.3 × 1.06 × 10^1

12.3 × 1.06 =13.038

13.038  × 10^1 = 1,3038  × 10^2

Hope this helps ^-^

Answer:

Combination 25 to 12

Step-by-step explanation:

[tex]C^{12} _{25}[/tex]

The expression 25! / [(25 - 12)! x 12!] represents the combination.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Let a be the number of items selected from the group of n.

We know that the combination is given by,

ⁿCₐ = n! / [(n - a)! x a!]

The expression is given below.

⇒ 25! / [(25 - 12)! x 12!]

Then the expression can be written as,

⇒ ²⁵C₁₂

Then the expression 25! / [(25 - 12)! x 12!] represents the combination.

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

#SPJ2

Answer:

Old adult

Step-by-step explanation:

Because about eighty percent of adult suffer from blood pressure.

Answer:

12m - 4

☆ putting the value of m in the above formula

12 × 4 - 4

= 48 - 4

= 44

6r - 4

☆ Putting the value of r in the above formula

6 × 6 - 4

= 36 - 4

= 32

Answer:

[tex] A(t) = 906 e^{0.012t}[/tex]

Where t is the number of months since the population was first recorded. And we want to find the population after 36 months so we need to replace t=36 months into the function and we got:

[tex] A(36) = 906 e^{0.012*36}= 1395.54[/tex]

So then we can conclude that after 36 months the population of mouse is between 1385 and 1396.

Step-by-step explanation:

We know that the population can be represented with this formula:

[tex] A(t) = 906 e^{0.012t}[/tex]

Where t is the number of months since the population was first recorded. And we want to find the population after 36 months so we need to replace t=36 monthsinto the function and we got:

[tex] A(36) = 906 e^{0.012*36}= 1395.54[/tex]

So then we can conclude that after 36 months the population of mouse is between 1385 and 1396.

Answer:

scale

Step-by-step explanation:

scales are used to measure weight

The tool that Caroline can use to Measure the mass of a dictionary is; Pan Balance.

When discussing measurements, there are different tools and equipment's that can be used such as  Ruler, Pan balance, Stopwatch, Liter container.

Now, the tools above can be used for measuring different things but our question wants the one that would be used to measure the mass of a dictionary and the correct tool is a Pan Balance.

Read more about Tools of Measurement at; https://brainly.com/question/17562905

#SPJ2

Answer:

57.45% increase

Step-by-step explanation:

The formula for percent change is (new - old)/new x 100.

The new value is $282 and the old value is $120.

Plug that into the formula:

(282 - 120)/282 x 100

= 57.45%

I hope this helped!

Answer:

16 cubic feet per hour

Step-by-step explanation:

We want to convert from cubic inch per minute to cubic feet per hour,

We can use the standard conversion rate:

1 cubic inch per minute = 0.0347222 cubic feet per hour

=> 462 cubic inch per minute = 462 * 0.0347222 = 16.04 cubic feet per hour

Approximating to whole number, it is 16 cubic feet per hour.

Answer:  Option  16 cubic feet

Step-by-step explanation:

1 meter = 1000mm

Convert the dimensions to mm:

1.5 x 1000 = 1500 mm

1.2 x1000 = 1200 mm

Area = length x width

Area = 1500 x 1200 = 1,800,000 square mm

Answer:

50 km

Step-by-step explanation:

As the figures are given similar ,

56/v = 84/75

v = 56 × 75/84

v = 50 km

Answer:

v = 50

Step-by-step explanation:

The trapezoids are similar, so set up a proportion like so:

[tex]\frac{56}{v} =\frac{84}{75}[/tex]

→Cross multiply:

[tex]\frac{4200}{84v}[/tex]

→Divide 4200 by 84:

v = 50

Answer:

{4*[6+(18-7)] } ÷1/3

{4*[6+18+7] }÷1/3

{24+72+28}÷1/3

{124}÷1/3

124*3/1

372/1=372

Answer: 4

Step-by-step explanation:

Given

[tex]F(x)=2x+4[/tex]

[tex]R(x)=x[/tex]

We need to find [tex]R(F(x))[/tex] at [tex]x=0[/tex]

[tex]R(F(x))=[2x+4][/tex]

[tex]R(F(x))=2x+4[/tex]

[tex]R(F(0))=2\times 1+4=4[/tex]

[tex]R(F(0))=4[/tex]

Answer:

63.2 = y

Step-by-step explanation:

The perimeter is the sum of all the sides

P = 7.8+ y+37.6 + y

171.8 = 7.8+ y+37.6 + y

Combine like terms

171.8 = 45.4 + 2y

Subtract 45.4 from both sides

171.8-45.4 = 45.4 + 2y -45.4

126.4 = 2y

Divide each side by 2

126.4/2 = 2y/2

63.2 = y

Answer:

A. 19 years old

Step-by-step explanation:

A  person at the age of 19 is probably still in college . He/She is probably investing more time and finance in his/her education. A person at age 19 is still building his or her career . He/she is  likely to have limited working experience. He/she has more years ahead of him to invest his little income(that is if he has any) for a longer term plan like owning a house and building a business.  

In fact at age 19 a person is more concern in his/her career development and studies. Buying a house is most likely a long time goal for a person of 19 years old because he has so many year ahead of him to gather or create wealth for himself.

The other ages 59, 79 and 69 years are individuals who have probably amassed wealth . They probably have over 3 decades of working experience and this working years will reflect in their savings. people at this age have shorter time to work or are probably even retired.

Answer:

A. 19 years old

Step-by-step explanation:

19 years old because usually by the time someone between the ages of 59 and 79 should already own or be renting a house if they have set their financial goals correctly.

Answer:

68.11% probability that the firm involved is firm B

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Cost overrun

Event B: Agency B used.

A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15.

This means that [tex]P(B) = 0.45[/tex]

From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively.

This means that [tex]P(A|B) = 0.14[/tex]

Probability of cost overrun.

Firm A is used 40% of the time, with 1% of these having cost overrun. B is used 45%, with 14% of these having cost overruns. C is used 15% of the time, with 17% of these having cost overruns.

So

[tex]P(A) = 0.4*0.01 + 0.45*0.14 + 0.15*0.17 = 0.0925[/tex]

What is the probability that the firm involved is firm B

[tex]P(B|A) = \frac{0.45*0.14}{0.0925} = 0.6811[/tex]

68.11% probability that the firm involved is firm B

Answer:

The mass of wood is 4309.65 kg.

Step-by-step explanation:

Volume of a cylinder is:

[tex]V = \pi r^{2} h[/tex]

Where [tex]r[/tex] is the radius of base of cylinder

and [tex]h[/tex] is the height of the cylinder

[tex]r=\dfrac{d}{2}[/tex]

[tex]d[/tex] is the diameter of base of cylinder.

A tree's trunk is in the shape of cylinder only. And we are given the following details:

[tex]d = 0.5m\\\Rightarrow r = \dfrac{0.5}{2} m[/tex]

[tex]h =36 m[/tex]

[tex]V = \pi (\dfrac{0.5}{2})^2 \times 36\\\Rightarrow V = 7.065\ m^3[/tex]

Density of wood of tree = 610 kg per cubic meter

Mass of trunk = Volume [tex]\times[/tex] density

[tex]\Rightarrow 610 \times 7.065\\\Rightarrow 4309.65\ kg[/tex]

Hence, mass of trunk is 4309.65 kg.

Answer:

325 mph and 420 mph

Step-by-step explanation:

If the speed of the slower plane is x, then the speed of the faster plane is x + 95.

The distance traveled by the slower plane is 3x.

The distance traveled by the faster plane is 3(x + 95).

The total distance is 2235 miles.

3x + 3(x + 95) = 2235

3x + 3x + 285 = 2235

6x = 1950

x = 325

x + 95 = 420

The speed of the planes is 325 mph and 420 mph.

Complete question:

Calculate each probability given that P(A) = 0.2, P(B) = 0.8, and A & B are independent.

a) compute P(A and B)

b) If P(A|B) = 0.7, compute P(A and B).

Answer:

(a) P(A and B) = 0.16

(b) P(A and B) = 0.56

Step-by-step explanation:

Two events are independent if occurrence of one event does not affect possibility of occurrence of another.

(a) if A and B are independent, then P(A and B) = P(A) x P(B)

                                                                               = 0.2 x 0.8

                                                                               = 0.16

(b)  If P(A|B) = 0.7, compute P(A and B)

Considering the notations of independent events,

[tex]P(A/B) = P(A)\\\\\frac{P(A \ and \ B)}{P(B)} = P(A)\\\\Thus, P(A/B) = \frac{P(A \ and \ B)}{P(B)}\\\\P(A \ and \ B) = P(A/B) *P(B)[/tex]

                     = 0.7 x 0.8

                     = 0.56

Answer:

A.

In 4231, the value of the digit 3 is 110 less than the value of the digit 3 in 3421.

Step-by-step explanation:

We can see that the value of 3 In 4231 is in ten while the value of 3 in 3421 is in thousands.

So to get the actual division factor, let's take 3300 and divide it by 30,

3300/30 = 110

So it's clear already, that the value of 3 in 4231 is 110 times less to the value in 3421

Answer: C In 4,231, the value of the digit 3 is 1/100 the value of the digit 3 in 3,421

Step-by-step explanation:

3,000 divided by 30 equals 100

Answer:

6 cm^2

Solution,

Volume of cube=1 cm^3

Volume of cube=l^3

or,1=(l)^3

or,l=1*1*1

length=2 cm

Again,

Surface area of cube= 6(a)^2

=6*(1)^2

=6*1

=6 cm^2

hope it helps

Good luck on your assignment