For some value of b, the expression 3(5x - 1) + b(2x - 7) is a constant. What is the constant?

The required Jodi will consume 180 calories if she eats 5 chocolates.

When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage. As gas costs increase, the cost of food may as well as well.

We can use proportionality to solve this problem. Since the number of calories consumed varies directly with the number of chocolates eaten, we can write:

calories consumed / chocolates eaten = constant

Let's call this constant k. We can solve for k using the information given:

72 calories / 2 chocolates = k

k = 36 calories/chocolate

Now we can use this constant to find the number of calories Jodi will consume if she eats 5 chocolates:

calories consumed / chocolates eaten = k

calories consumed / 5 chocolates = 36 calories/chocolate

calories consumed = 5 chocolates * 36 calories/chocolate

calories consumed = 180 calories

Therefore, Jodi will consume 180 calories if she eats 5 chocolates.

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Answer: Neither (look at the image for the solution)

Step-by-step explanation:

Answer: parallel

Step-by-step explanation:

look at the lines and u can see two lines so parallel

The total number of each type of bill and coin are

$5 bills x 5,

$1 bills x 10,

quarters x 16,

dimes x 9.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) sign on either side. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.

Now in the given question,

$5 bills = x, total = 5x

$1 bills = 2x, total = x

Quarters = 3x + 1, total = 0.25(3x + 1)

Dimes = 3x + 1 - 7= 3x - 6, total = 0.1(3x - 6)

Equation below as the sum, solve for x:

5x + 2x + 0.25(3x + 1) + 0.1(3x - 6) = 39.9

7x + 0.75x + 0.25 + 0.3x - 0.6 = 39.9

8.05x  - 0.35 = 39.9

8.05x = 40.25

x = 40.25/8.05

x = 5

Number of each bill and coin:

$5 bills = 5

$1 bills = 2*5 = 10

Quarters = 3*5 + 1 = 16

Dimes = 3*5 - 6 = 9

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It will take 10 years for the account to reach $200, as determined by solving the equation A = [tex]325(1 + 0.047/12)^(12t)[/tex] for t.

[tex]A = 325(1+0.047/12)^(12t)[/tex]

[tex]200 = 325(1+0.047/12)^(12t)[/tex]

[tex]200/325 = (1+0.047/12)^(12t)[/tex]

[tex]log_((1+0.047/12))(200/325) = 12t[/tex]

[tex]t = log_((1+0.047/12))(200/325) / 12[/tex]

t = 8.75 years

It will take 9 years for the account to reach $200.

Hassan deposited $325 into an account that pays 4.7% annual interest compounded monthly. We can use a system of equations to determine how many years it will take for the account to reach $200. To do this, we first write an equation to represent Hassan's account balance A after t years. This equation is[tex]A = 325(1+0.047/12)^(12t)[/tex]. We then solve for t by taking the logarithm of both sides, which gives us means that it will take 8.75 years for the account to reach $200, which we round up to 9 years.

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The solution is, Option a

Stratified random sample

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

here, we have,

Explanation:

(a) In stratified random sampling, a division of the population occurs in such a way that a population is stratified in different small groups or strata with common traits and same proportion both in population and sample. this type of sample so formed is known as stratified random sample.

(b) Simple random Sample:

This sample is formed by the random and unbiased selection of individual that represents the population.

(c) Population:

The entire set of individuals with certain specific characteristics represents a population whereas a sample is drawn out of the population and can be referred to as the subset of the population.

(d) Cluster Sample:

In this, separate sample groups are formed known as clusters, here sampling of random clusters take place.

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The probability that a student ordered a hamburger and a Slurpee is Option D) 23 over 137.

Generally, To find the probability that a student ordered a hamburger and a Slurpee, we need to divide the number of students who ordered a hamburger and a Slurpee by the total number of students.

From the table, we can see that 23 students ordered a salad and a water.

There were a total of 38 + 12 + 14 + 18 + 28 + 7 + 23 = 137 students in the cafeteria.

Therefore, the probability that a student ordered a salad and a water is 23/137, or about 0.17.

Therefore, the correct answer is d) 23 over 137.

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Answer:

Step-by-step explanation:

To find the volume of the container, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. Plugging in the given values, we get:

V = π * 8.1^2 * 17.9 = 1146.4 cm^3

Since the sample contains 0.04 g of the trace element per cubic centimeter of water, the amount of trace element in the entire container can be found by multiplying the volume of the container by the concentration of the trace element:

0.04 g/cm^3 * 1146.4 cm^3 = 45.86 g

So Samir has collected approximately 45.9 g of the trace element, rounded to the nearest tenth.

Answer:147.6g

Step-by-step explanation

The dimensions will be as follows;

width is 5cm while the length is 20cm.

Let width = w

Let length = 4w (according to question)

Perimeter = 50cm

Perimeter formula for a rectangle = 2 (l +w)

Substituting in the variables (width and length)

2(w + 4w) = 50

2(5w) = 50

10w = 50

w = 5

Remember that length = 4w

length = 4w

length = 4(5)

length = 20cm

Therefore, the dimensions of the rectangle are 5cm by 20 cm.

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The equation of the given information is y(x) = 5x+10

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

Given that cost of renting for different numbers of hours.

The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.

Therefore, the cost (y) of renting a paddle boat for 'x' hours is:

y(x) = 5x+10

here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.

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Answer:

  6 years

Step-by-step explanation:

You want the length of time it takes for a $50 investment to total $3200 if it doubles in value each year.

The value of the investment can be described by ...

  v = 50·2^t

where t is the number of years.

You want t when v=3200:

  3200 = 50·2^t

  64 = 2^t

  log(64) = t·log(2) . . . . . take logarithms

  t = log(64)/log(2) = 6

It will take 6 years for her investment to reach $3200.

__

Additional comment

If you're familiar with powers of 2, you recognize that 64 = 2⁶. Comparing exponents in ...

  64 = 2^t

  2^6 = 2^t . . . . . use 2^6 for 64

we can see that t=6. The logarithms are used to formalize this comparison.

Answer:

100 dispenses

Step-by-step explanation:

To check the answer:

Gumballs: 200 - (1*100) = 100

Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.

Chocolate Candies: 900 - (8*100) = 100

Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.

Answer:

  100

Step-by-step explanation:

Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.

The number of remaining gumballs after d dispenses is ...

  g = 200 -d

The number of remaining chocolates after d dispenses is ...

  c = 900 -8d

The number remaining in each machine will be equal when ...

  g = c

  200 -d = 900 -8d . . . . . substitute the above expressions

  7d = 700 . . . . . . . . . . add 8d -200

  d = 100 . . . . . . . . . divide by 7

100 dispenses from each machine will make the number of candies in the machines equal.

V Prism is V = B × h=9.5*4=38

the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47

V=10.47+38=48.476

A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.

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Answer:

a sea monkey weighs 6.6oz

Step-by-step explanation:

To find the balance of the account at the end of the week, we need to calculate all the transactions:

Initial balance: $150

Shoes: -$180

Cash advance: +$300

Repaid debt: -$250

Bank fee: +$110

Cash deposit: -$150

So the final balance would be $150 - $180 + $300 - $250 + $110 - $150 = $-70.

This means the balance of the account at the end of the week would be -$70.

Tammy received 19 phone calls on the first evening, 13 phone calls on the second evening, and 76 phone calls on the third evening.

Let's use algebra to solve the problem.

Let x be the number of phone calls Tammy received on the first evening.

According to the problem, she received 6 fewer calls on the second evening than on the first evening. This means that the number of phone calls she received on the second evening is x - 6.

The problem also states that she received 4 times as many calls on the third evening as she did on the first evening. This means that the number of phone calls she received on the third evening is 4x.

We know that Tammy received a total of 108 phone calls over the three evenings. We can use this information to set up an equation:

x + (x - 6) + 4x = 108

Simplifying the equation:

6x - 6 = 108

Adding 6 to both sides:

6x = 114

Dividing both sides by 6:

x = 19

Therefore, Tammy received 19 phone calls on the first evening, 13 phone calls (19 - 6) on the second evening, and 76 phone calls (4 x 19) on the third evening.

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Complete question is:

Over the last three evenings, Tammy received a total of 108 phone calls at the call center. The second evening, she received 6 fewer calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?

The solution to the equation 6(72(x - 2)) = 4(15 - 3x) is x = 77/37.

Given the equation in the question

6(72(x - 2)) = 4(15 - 3x)

To solve the equation, remove the parenthesis by applying distributive property.

6( 72 × x - 72 × 2 ) = 4 × 15 - 4 × 3x

6( 72x - 144 ) = 60 - 12x

6( 72x - 144 ) = 60 - 12x

6 × 72x - 6 × 144 = 60 - 12x

432x - 864 = 60 - 12x

Collect like terms

Add -12x to both sides

432x + 12x - 864 = 60 - 12x + 12x

432x + 12x - 864 = 60

Add 864 to both sides

432x + 12x - 864 + 864 = 60 + 864

432x + 12x = 60 + 864

444x = 924

x = 924/444

x  = 77/37

Therefore, the value of x is 77/37.

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The correct equations for the measures of the unknown angles x and y are:

x = cos(a), y = sin(a).

The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:

sin(a) = opposite side / hypotenuse

cos(a) = adjacent side / hypotenuse

tan(a) = opposite side / adjacent side

In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).

The inverse trigonometric functions[tex](sin^-1, cos^-1, tan^-1)[/tex] are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:

[tex]sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))[/tex]

So, the correct equations for the measures of the unknown angles x and y are:

[tex]x = cos^-1(x)y = sin^-1(y)[/tex]

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Answer:

The main cause of deforestation is agriculture (poorly planned infrastructure is emerging as a big threat too) and the main cause of forest degradation is illegal logging. In 2019, the tropics lost close to 30 soccer fields' worth of trees every single minute

Answer:

i) 84

ii) 7

iii) 47

iv) 16

v) 56

vi) 54

Step-by-step explanation:

The easiest way to understand this problem visually is to create a Venn diagram (See attached diagrams below to help you)

First, note that the total amount of people with each condition beside the relevant circle. Then, since 15 have all 3, write 15 in the center.

We're told 35 had arthritis and arteriosclerosis, and 15 had all 3, so the amount with arthritis and arteriosclerosis only is 25-25=20. So we write 20 in the crosssection between arthritis and arteriosclerosis that doesn't include loss of hearing.

We're told 33 had arthritis and loss of hearing, and 15 had all 3, so the amount with arthritis and loss of hearing but not arteriosclerosis is 33-15=18. So we write 18 in the crosssection between arthritis and loss of hearing that doesn't include arteriosclerosis.

We're told 31 had arteriosclerosis and loss of hearing, and 15 had all 3, so the amount with arteriosclerosis and loss of hearing only is 31-15=16. So we write 16 in the crosssection between arteriosclerosis and loss of hearing that doesn't include arthritis.

(see diagram A to see how this should look)

70 people have arthritis and (18+25+20=63) have arthritis and another condition, so the amount with only arthritis is 70-63=7

60 people have arteriosclerosis and (20+15+16=51) have arteriosclerosis and another condition, so the amount with only arteriosclerosis is 60-51=9

80 people have loss of hearing and (18+15+16=49) have loss of hearing and another condition, so the amount with only loss of hearing is 80-49=31

Marking in these figures completes the diagram (See diagram B to see how it should look)

i)

The total amount of people represented within the diagram (ie, the ones with conditions) is 7+20+9+18+15+16+31=116. If 200 were surveyed, this means the amount without these conditions is 200-116=84

ii)

Above, we found the amount with arthritis only was 7

iii)

7 have only arthrits, 9 have only arteriosclerosis, and 31 have only  loss of hearing , so the amount with only one ailment is 7+9+31=47

iv)

Above, we found that 16 had arteriosclerosis and loss of hearing but not arthritis

v)

The amount with arteriosclerosis or loss of hearing but not arthritis is equal to the amount with arteriosclerosis only plus the amount with loss of hearing plus the amount with both arteriosclerosis and loss of hearing: 9+31+16=56

vi)

Above, we found the amount with arthritis and arteriosclerosis only is 20, the amount with arthritis and loss of hearing but not arteriosclerosis is 18, and the amount with amount with arteriosclerosis and loss of hearing only is 16. So the total amount with exactly two conditions is 20+18+16=54

Answer:

So, the rational number is [tex]\frac{52}{12}[/tex] .

Step-by-step explanation:

Let x be the other number.

We know ,

[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]

To find x, we need to convert both to have a common denominator.

So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex]  ,

[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]

After multiplication the fraction  [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex]  .

[tex]\frac{70}{360}[/tex]+ x =  [tex]\frac{56}{10}[/tex]

Now we have common denominator of 360in both fraction,

Now,

we can simplify the equation ,

[tex]\frac{70}{360}[/tex]  + x = [tex]\frac{56}{10}[/tex]

70 + 360x = 56 × 36

2520 + 360x = 2016

504 + 360x = 2016

360x = 1512

x = [tex]\frac{1512}{360}[/tex]

   =[tex]\frac{52}{12}[/tex]

So, the rational number is [tex]\frac{52}{12}[/tex] .

The parabola's shape is influenced by the separation between its focus and vertex. The parabola becomes wider as the vertex is focused further away (flatter).

A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line. The parabola's directrix serves as the fixed line, while the focus, represented by the letter F, serves as the fixed point. The line through the F and perpendicular to the directrix is the parabola's axis.

2. As illustrated here, the parabola's shape is influenced by the separation between its focus and vertex.

The parabola becomes wider as the vertex is focused further away (flatter).

The parabola becomes thinner as the vertex comes into focus (steeper).

3. If a > 0 in the quadratic equation the parabola opens upward and if a< 0 then the parabola opens downward.

4. The vertex of the parabola is the location where it crosses the axis.

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There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.

If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:

C(n + k - 1, k - 1)

where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:

C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)

There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:

C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55

Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars

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There are 20 different combinations of committees that can be formed since no person can serve on more than one committee.

In order to form committees of 4, 3, and 2 people, we must first determine how many combinations are possible. There are 9 people in total, so the first committee must consist of 4 people. That leaves 5 people. The second committee must consist of 3 people, leaving 2 people for the final committee. To calculate the total number of combinations, we must multiply the number of choices for each committee. For the first committee, there are 9C4 combinations, for the second committee there are 5C3 combinations, and for the third committee there are 2C2 combinations. Multiplying these together, we obtain 9C4 x 5C3 x 2C2 = 20 combinations. Therefore, there are 20 different combinations of committees that can be formed since no person can serve on more than one committee.

The complete question: A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many can be formed if no person can serve on more than one committee?

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The value of x in the diagram is given as follows:

x = 10.

Similar triangles share these two features:

Considering the similar triangles, the proportional relationship for the side lengths is given as follows:

6/(6 + x) = (x - 1)/(2x + 4).

Applying cross multiplication, the value of x is obtained as follows:

(x - 1)(x + 6) = 6(2x + 4)

x² + 5x - 6 = 12x + 24

x² - 7x - 30 = 0.

Factoring, we obtain the solutions are follows:

(x - 10)(x + 3) = 0.

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Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0

Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this :  [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.

Answer: x = 22

Step-by-step explanation:

Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22

Answer:

Step-by-step explanation:

The measures regarding the angles of the triangle are given as follows:

The angle measures are defined as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the value of x is obtained as follows:

5x - 14 + x - 5 + 2x - 9 = 180

8x = 208

x = 208/8

x = 26.

Then the measures are given as follows:

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