1. Translate the variable expression into a word phrase: 4b – 2
Translate the word phrase into a variable expression:
2. the sum of 16 and 4 times a number
3. Write an equation for the following word problem. Use b for the number of boys and g for the number of girls.
There are eight fewer boys than girls in Mrs. Davis' class. How many boys are in the class?
4. Will the standard form 3.2 × 10–4 be more or less than 1? Explain what effect the negative exponent has.
5.Use a five-step plan to solve the following word problem. Show all five steps in your response:

Doug is twice Anne's age. Doug is 34 years old. How old is Anne?

Answer:

The domain of the function is {0,1,2,3,4} and the range of the function is {$33, $44, $55, $66, $77}

Step-by-step explanation:

Consider the provided information.

Sarah has sold $33 worth of tickets sales to the comedy show. She has 4 tickets left to sell at $11 per hour.

First write the function as shown.

Let the number of tickets are x and she already sold $33 worth of tickets.

Therefore the function is: [tex]f(x)=11t+33[/tex]

For t=0

[tex]f(0)=11(0)+33=33[/tex]

For t=1

[tex]f(1)=11(1)+33=44[/tex]

For t=2

[tex]f(2)=11(2)+33=55[/tex]

For t=3

[tex]f(3)=11(3)+33=66[/tex]

For t=4

[tex]f(4)=11(4)+33=77[/tex]

Hence, the domain of the function is {0,1,2,3,4} and the range of the function is {$33, $44, $55, $66, $77}

The number of friends that were called on Sunday are 27 friends.

On Friday, the number of friends Sharon called = 3 friends

On Saturday, the number of each of those 3 friends called 3 different friends.

Therefore the number of friends on Saturday = 3×3

= 9

The number of friends called on Sunday = 9 × 3

= 27

Therefore the number of friends called on Sunday= 27

Learn more here:

https://brainly.com/question/12353086

The product of nine and the sum of a number Z and four can be written as 9(Z + 4). For example, if Z = 5, then the expression becomes 9(5 + 4), which equals 81.

The product of nine and the sum of a number Z and four can be written as 9(Z + 4).

For example, if Z = 5, then the expression becomes 9(5 + 4), which equals 9(9) = 81.

So, the product of nine and the sum of a number Z and four is 9(Z + 4), where Z represents any number.

Answer:

Point-slope form: An equation of a straight line in the form [tex]y -y_1 = m(x -x_1)[/tex];  

where

m is the slope of the line and [tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.

Given the equation: [tex]y-2=-\frac{3}{4}(x-6)[/tex]         ......[1]

On comparing with Point slope form equation we have;

m = [tex]-\frac{3}{4}[/tex] and point (6 , 2)

Now, find the Intercept of the given equation:

x-intercept: The graph crosses the the x-axis i.e,

Substitute y =0 in [1] and solve for x;

[tex]0-2=-\frac{3}{4}(x-6)[/tex]

[tex]-2=-\frac{3}{4}(x-6)[/tex]

Using distributive property:  [tex]a\cdot(b+c) = a\cdot b +a\cdot c[/tex]

[tex]-2 = -\frac{3}{4}x + \frac{18}{4}[/tex]

Subtract [tex]\frac{18}{4}[/tex] on both sides we get;

[tex]-2-\frac{18}{4}= -\frac{3}{4}x + \frac{18}{4} -\frac{18}{4} [/tex]

Simplify:

[tex]-\frac{26}{4} = -\frac{3}{4}x[/tex]

or

-26 = -3x

Divide both sides by -3 we get;

x = 8.667

x-intercept: (8.667, 0)

Similarly, for

y-intercept:

Substitute x = 0 in [1] and solve for y;

[tex]y-2=-\frac{3}{4}(0-6)[/tex]

[tex]y-2=\frac{18}{4}[/tex]

Add 2 on both sides we get;

[tex]y-2+2=\frac{18}{4}+2[/tex]

Simplify:

 [tex]y=\frac{26}{4} =6.5[/tex]

y-intercept: (0, 6.5)

Now, using these two points (8.667, 0) and (0, 6.5) you can plot the graph using line tool as shown below.

Answer:

Your answer is B

Answer:

$750 at $10 per poster

Step-by-step explanation:

Let amount of water that , my dog's water bowl can hold=x cubic unit

Level of water upto which my dog's water bowl is filled

                                 [tex]=\frac{3x}{4} \text{Cubic unit}[/tex]

Let amount of water drank by my Dog in a drink=y cubic unit

   Writing the statement in terms of equation

    [tex]\frac{3x}{4}-y=\frac{x}{3}\\\\y=\frac{3x}{4}-\frac{x}{3}\\\\y=\frac{9x-4x}{4 \times 3}\\\\y=\frac{5x}{12}[/tex]

Fraction of the bowl did my dog drank is equal to [tex]\frac{5}{12}[/tex]

There are 36 different arrays that Vince can draw to represent the total number of beads he has. The sizes of the arrays range from 1 to 16 beads.

To find the different arrays Vince can draw to represent the total number of beads he has, we need to consider all the possible ways he can arrange the beads. Essentially, we are looking for all the possible partitions of 16.

A partition of a number represents the different ways it can be expressed as a sum of positive integers. In this case, we want to find all the partitions of 16.

To do this, we can list all the possible sizes of arrays that Vince can draw. Here are the possible sizes:

16

15 + 1

14 + 2

13 + 3

12 + 4

11 + 5

10 + 6

9 + 7

8 + 8

14 + 1 + 1

13 + 2 + 1

12 + 3 + 1

11 + 4 + 1

10 + 5 + 1

9 + 6 + 1

8 + 7 + 1

12 + 2 + 2

11 + 3 + 2

10 + 4 + 2

9 + 5 + 2

8 + 6 + 2

7 + 7 + 2

10 + 3 + 3

9 + 4 + 3

8 + 5 + 3

7 + 6 + 3

6 + 6 + 4

9 + 3 + 3 + 1

8 + 4 + 3 + 1

7 + 5 + 3 + 1

6 + 6 + 3 + 1

8 + 3 + 3 + 2

7 + 4 + 3 + 2

6 + 5 + 3 + 2

5 + 5 + 4 + 2

7 + 3 + 3 + 3

6 + 4 + 3 + 3

5 + 5 + 3 + 3

4 + 4 + 4 + 4

So, there are 36 different arrays that Vince can draw to represent the total number of beads he has. The sizes of the arrays range from 1 to 16 beads.

Learn more about arrays click;

https://brainly.com/question/33609476

#SPJ12

Answer with Step-by-step explanation:

1. x-7>10

Adding 7 on both sides,we get

x>17

2. 3x ≤ 21

Dividing both sides by 3,we get

x≤7

3. 5a-2<18

Adding 2 on both sides, we get

5a<20

Dividing both sides by 5,we get

a<4

4. 2t + 8 ≥ -4(t+1)

Distributing -4 on right hand side of inequality

2t+8 ≥ -4t-4

2t+4t ≥ -4-8

6t ≥  -12

Dividing both sides by 6, we get

t ≥ -2

If Marco wants to set up 12 small turbines with 3 blades each. If 4 wind turbines blades cost $79.64 then $716.76 costs for all blades.

Two or more expressions connected with an equal sign is called ad equation.

Given Marco wants to set up 12 small turbines with 3 blades each. If 4 wind turbines blades cost $79.64, then we have to find the cost of all blades.

Each turbine has 3 blades, so for 12 tubines we have

3×12=36 blades.

If 4 blades cost is  $79.64, then we have to find cost of 36 blades.

Let y be the cost of 36 blades.

4 /36= 79.64/y

Use cross multiplication,

4 * y = 36 * 79.64

4y = 2,867.04

y=716.76

Therefore 36 blades cost is $ 716.76.

To learn more on equations click:

https://brainly.com/question/10413253

#SPJ2

The number of batches you can make if you use all the sugar is 12.61 batches.

The cost of sugar used per batch is $0.28.

A 4-pound bag of sugar = 454 one-teaspoon

Sugar used for a batch of muffins = ¾ cup

If 1 cup = 48 teaspoons

3/4 cup = 3/4 × 48

= 36 teaspoons

Number of batches to make = 454 one-teaspoon / 36 teaspoons

= 12.61 batches

Cost of sugar teaspoons= 3.49/454

= $0.007687224669603 per teaspoon

Cost of sugar per batch = 0.007687224669603 × 36

= $0.276740088105726 per batch

Hence, the cost of sugar used per batch is approximately $0.28

Read more on weight:

https://brainly.com/question/229459

#SPJ1

A 4-pound bag of sugar contains 454 one-teaspoon servings and costs $3.49. A batch of muffins uses ¾ cup of sugar. How many batches can you make if you use all the sugar? What is the cost of sugar for each batch? (1 cup = 48 teaspoons)

To find out how many batches of muffins can be made and the cost per batch, convert the total servings of sugar to cups, then divide by the amount of sugar used per batch, and finally, divide the total cost by the number of batches. which results in approximately $0.29 per batch.

The subject of this question is Mathematics, and it appears to be at the High School level due to the application of ratios, conversions, and basic algebraic skills to solve real-world problems.

Calculating Batches of Muffins from a Sugar Bag

Firstly, we determine the total amount of sugar in the bag in terms of cups. Since 1 teaspoon is equivalent to 4 grams of sugar, and we have 454 servings, we multiply 454 by 4g to get 1816g of sugar in total. To convert grams to cups (given 1 cup of sugar is 200g), we divide 1816g by 200g/cup, which gives us 9.08 cups.

Since a batch of muffins uses 3/4 cup of sugar, we divide the total cups of sugar by 3/4 to find the number of batches. 9.08 cups divided by 3/4 cups per batch results in approximately 12.1 batches; however, since you can't make a partial batch with the remaining sugar, it is safe to say you can make 12 full batches. To find the cost per batch, divide the total cost of the bag ($3.49) by the number of batches (12), which results in approximately $0.29 per batch.

7 cups

4 1/5= 21/5

3+3+3+3+3+3+3= 21

             7

Jessica can fill 7 glasses with water, by dividing the total amount of water ([tex]4\frac{1}{5}[/tex] cups) by the amount that each glass holds ([tex]\frac{3}{5}[/tex] cup).

The question asks us to determine how many glasses Jessica can fill with water when each glass holds [tex]\frac{3}{5}[/tex] cup of water and she has 4 1/5 cups of water in total. To solve this, we need to divide the total amount of water by the amount each glass holds.

Firstly, we need to convert the mixed number 4 1/5 cups to an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator, like this: (4 times 5) + 1 = 21, so 4 1/5 cups is the same as [tex]\frac{21}{5}[/tex]cups.

Next, we divide the total amount of water (21/5 cups) by the amount each glass holds ([tex]\frac{3}{5}[/tex] cup), which can be written as a fraction division problem:

[tex]\frac{\frac{21}{5} }{\frac{3}{5} }[/tex] = [tex]\frac{21}{5}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{21}{3}[/tex] = 7

So, Jessica can fill 7 glasses with water.

A prototype is unique in that it is designed to have functional features similar to the final product, allowing designers and engineers to test and refine the design. Option D.

The main difference between a prototype and other kinds of models is that a prototype is designed to have some features that work like the real thing (Option D).

Answer:

C.

Step-by-step explanation:

The ordered pair which represents the point on the line y = 2x + 1 is C. (-1, -1).

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

Given equation is y = 2x + 1.

We have to substitute each of the points in the line if the equation holds or not.

A. (0, 3)

2x + 1 = 0 + 1 = 1 ≠ 3

B. (2, 1)

2x + 1 = 4 + 1 = 5 ≠ 1

C. (-1, -1)

2x + 1 = -2 + 1 = -1

D. (1, 2)

2x + 1 = 2 + 1 = 3 ≠ 2

Hence the point on the line is C. (-1, -1).

Learn more about Lines here :

https://brainly.com/question/2564656

#SPJ2

Answer:

27.7 or 28

Step-by-step explanation:

Answer:

[tex]\texttt{Submarine's depth relative to sea level after the first minute = }-\frac{4}{15} miles[/tex]

Step-by-step explanation:

Starting at sea level, a submarine descended at a constant rate to a depth of −4/5 mile relative to sea level in 3 minutes.

Total time = 3 minutes

[tex][tex]\texttt{Total depth descended in 3 minutes = }-\frac{4}{5}miles[/tex][/tex]

We need to find what was the submarine's depth relative to sea level after the first minute,

[tex]\texttt{Depth descended in per minute = }-\frac{\frac{4}{5}}{3}=-\frac{4}{15}miles[/tex]

[tex]\texttt{Submarine's depth relative to sea level after the first minute = }-\frac{4}{15}\times 1=-\frac{4}{15} miles\\\\\texttt{Submarine's depth relative to sea level after the first minute = }-\frac{4}{15} miles[/tex]